results for au:Berger_B in:gr-qc

- Mar 01 2018 gr-qc astro-ph.CO arXiv:1802.10194v2The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually-unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically-polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy-densities of tensor, vector, and scalar modes at 95% credibility to $\Omega^T_0 < 5.6 \times 10^{-8}$, $\Omega^V_0 < 6.4\times 10^{-8}$, and $\Omega^S_0 < 1.1\times 10^{-7}$ at a reference frequency $f_0 = 25$ Hz.
- Feb 15 2018 gr-qc arXiv:1802.05241v1We report on a new all-sky search for periodic gravitational waves in the frequency band 475-2000 Hz and with a frequency time derivative in the range of [-1.0e-8, +1e-9] Hz/s. Potential signals could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO's first observational run O1. No gravitational wave signals were observed, and upper limits were placed on their strengths. For completeness, results from the separately published low frequency search 20-475 Hz are included as well. Our lowest upper limit on worst-case (linearly polarized) strain amplitude h_0 is 4e-25 near 170 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of 1.3e-24. For a circularly polarized source (most favorable orientation), the smallest upper limit obtained is ~1.5e-25.
- Dec 05 2017 gr-qc astro-ph.CO arXiv:1712.01168v2Cosmic strings are topological defects which can be formed in GUT-scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension $G\mu$ and the intercommutation probability, using not only the burst analysis performed on the O1 data set, but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and Big-Bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider.
- Nov 21 2017 gr-qc astro-ph.HE arXiv:1711.06843v1We present the results of a search for long-duration gravitational wave transients in the data of the LIGO Hanford and LIGO Livingston second generation detectors between September 2015 and January 2016, with a total observational time of 49 days. The search targets gravitational wave transients of \unit[10 -- 500]s duration in a frequency band of \unit[24 -- 2048]Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. No significant events were observed. %All candidate triggers were consistent with the expected background, As a result we set 90\% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. We also show that the search is sensitive to sources in the Galaxy emitting at least $\sim$ \unit[$10^{-8}$]$\mathrm{M_{\odot} c^2}$ in gravitational waves.
- Nov 16 2017 astro-ph.HE gr-qc arXiv:1711.05578v1On June 8, 2017 at 02:01:16.49 UTC, a gravitational-wave signal from the merger of two stellar-mass black holes was observed by the two Advanced LIGO detectors with a network signal-to-noise ratio of 13. This system is the lightest black hole binary so far observed, with component masses $12^{+7}_{-2}\,M_\odot$ and $7^{+2}_{-2}\,M_\odot$ (90% credible intervals). These lie in the range of measured black hole masses in low-mass X-ray binaries, thus allowing us to compare black holes detected through gravitational waves with electromagnetic observations. The source's luminosity distance is $340^{+140}_{-140}$ Mpc, corresponding to redshift $0.07^{+0.03}_{-0.03}$. We verify that the signal waveform is consistent with the predictions of general relativity.
- Oct 26 2017 astro-ph.HE gr-qc arXiv:1710.09320v1The first observation of a binary neutron star coalescence by the Advanced LIGO and Advanced Virgo gravitational-wave detectors offers an unprecedented opportunity to study matter under the most extreme conditions. After such a merger, a compact remnant is left over whose nature depends primarily on the masses of the inspiralling objects and on the equation of state of nuclear matter. This could be either a black hole or a neutron star (NS), with the latter being either long-lived or too massive for stability implying delayed collapse to a black hole. Here, we present a search for gravitational waves from the remnant of the binary neutron star merger GW170817 using data from Advanced LIGO and Advanced Virgo. We search for short ($\lesssim1$ s) and intermediate-duration ($\lesssim 500$ s) signals, which includes gravitational-wave emission from a hypermassive NS or supramassive NS, respectively. We find no signal from the post-merger remnant. Our derived strain upper limits are more than an order of magnitude larger than those predicted by most models. For short signals, our best upper limit on the root-sum-square of the gravitational-wave strain emitted from 1--4 kHz is $h_{\rm rss}^{50\%}=2.1\times 10^{-22}$ Hz$^{-1/2}$ at 50% detection efficiency. For intermediate-duration signals, our best upper limit at 50% detection efficiency is $h_{\rm rss}^{50\%}=8.4\times 10^{-22}$ Hz$^{-1/2}$ for a millisecond magnetar model, and $h_{\rm rss}^{50\%}=5.9\times 10^{-22}$ Hz$^{-1/2}$ for a bar-mode model. These results indicate that post-merger emission from a similar event may be detectable when advanced detectors reach design sensitivity or with next-generation detectors.
- Oct 17 2017 gr-qc arXiv:1710.05837v1The LIGO Scientific and Virgo Collaborations have announced the first detection of gravitational waves from the coalescence of two neutron stars. The merger rate of binary neutron stars estimated from this event suggests that distant, unresolvable binary neutron stars create a significant astrophysical stochastic gravitational-wave background. The binary neutron star background will add to the background from binary black holes, increasing the amplitude of the total astrophysical background relative to previous expectations. In the Advanced LIGO-Virgo frequency band most sensitive to stochastic backgrounds (near 25 Hz), we predict a total astrophysical background with amplitude $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.8_{-1.3}^{+2.7} \times 10^{-9}$ with $90\%$ confidence, compared with $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.1_{-0.7}^{+1.2} \times 10^{-9}$ from binary black holes alone. Assuming the most probable rate for compact binary mergers, we find that the total background may be detectable with a signal-to-noise-ratio of 3 after 40 months of total observation time, based on the expected timeline for Advanced LIGO and Virgo to reach their design sensitivity.
- Oct 09 2017 gr-qc astro-ph.IM arXiv:1710.02185v3The first observing run of Advanced LIGO spanned 4 months, from September 12, 2015 to January 19, 2016, during which gravitational waves were directly detected from two binary black hole systems, namely GW150914 and GW151226. Confident detection of gravitational waves requires an understanding of instrumental transients and artifacts that can reduce the sensitivity of a search. Studies of the quality of the detector data yield insights into the cause of instrumental artifacts and data quality vetoes specific to a search are produced to mitigate the effects of problematic data. In this paper, the systematic removal of noisy data from analysis time is shown to improve the sensitivity of searches for compact binary coalescences. The output of the PyCBC pipeline, which is a python-based code package used to search for gravitational wave signals from compact binary coalescences, is used as a metric for improvement. GW150914 was a loud enough signal that removing noisy data did not improve its significance. However, the removal of data with excess noise decreased the false alarm rate of GW151226 by more than two orders of magnitude, from 1 in 770 years to less than 1 in 186000 years.
- Oct 09 2017 gr-qc astro-ph.HE arXiv:1710.02327v2Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, \it narrow-band analyses methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of eleven pulsars using data from Advanced LIGO's first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched: in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far.
- Sep 28 2017 gr-qc arXiv:1709.09203v1We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously-published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.
- Sep 28 2017 gr-qc astro-ph.HE arXiv:1709.09660v3On August 14, 2017 at 10:30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm-rate of $\lesssim$ 1 in 27000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are $30.5_{-3.0}^{+5.7}$ Msun and $25.3_{-4.2}^{+2.8}$ Msun (at the 90% credible level). The luminosity distance of the source is $540_{-210}^{+130}~\mathrm{Mpc}$, corresponding to a redshift of $z=0.11_{-0.04}^{+0.03}$. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg$^2$ using only the two LIGO detectors to 60 deg$^2$ using all three detectors. For the first time, we can test the nature of gravitational wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.
- Jul 11 2017 gr-qc astro-ph.IM arXiv:1707.02667v2We report on an all-sky search for periodic gravitational waves in the frequency band 20-475 Hz and with a frequency time derivative in the range of [-1.0, +0.1]e-8 Hz/s. Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO's first observational run, O1. No periodic gravitational wave signals were observed, and upper limits were placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude h0 are 4e-25 near 170 Hz. For a circularly polarized source (most favorable orientation), the smallest upper limits obtained are 1.5e-25. These upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest upper limits obtained for the strain amplitude are 2.5e-25.
- Jul 11 2017 gr-qc arXiv:1707.02669v2We report results of a deep all-sky search for periodic gravitational waves from isolated neutron stars in data from the first Advanced LIGO observing run. This search investigates the low frequency range of Advanced LIGO data, between 20 and 100 Hz, much of which was not explored in initial LIGO. The search was made possible by the computing power provided by the volunteers of the Einstein@Home project. We find no significant signal candidate and set the most stringent upper limits to date on the amplitude of gravitational wave signals from the target population, corresponding to a sensitivity depth of 48.7 [1/$\sqrt{{\textrm{Hz}}}$]. At the frequency of best strain sensitivity, near 100 Hz, we set 90% confidence upper limits of $1.8 \times 10^{-25}$. At the low end of our frequency range, 20 Hz, we achieve upper limits of $3.9 \times 10^{-24}$. At 55 Hz we can exclude sources with ellipticities greater than $10^{-5}$ within 100 pc of Earth with fiducial value of the principal moment of inertia of $10^{38} \textrm{kg m}^2$.
- Jun 13 2017 astro-ph.HE gr-qc arXiv:1706.03119v3We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using data from the first Advanced LIGO observing run. The search method uses details of the modelled, parametrized continuous signal to combine coherently data separated by less than a specified coherence time, which can be adjusted to trade off sensitivity against computational cost. A search was conducted over the frequency range from 25 Hz to 2000 Hz, spanning the current observationally-constrained range of the binary orbital parameters. No significant detection candidates were found, and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections. The most stringent upper limit was set at 175 Hz, with comparable limits set across the most sensitive frequency range from 100 Hz to 200 Hz. At this frequency, the 95 pct upper limit on signal amplitude h0 is 2.3e-25 marginalized over the unknown inclination angle of the neutron star's spin, and 8.03e-26 assuming the best orientation (which results in circularly polarized gravitational waves). These limits are a factor of 3-4 stronger than those set by other analyses of the same data, and a factor of about 7 stronger than the best upper limits set using initial LIGO data. In the vicinity of 100 Hz, the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model, depending on inclination angle, if the most likely inclination angle of 44 degrees is assumed, they are within a factor of 1.7.
- Jun 07 2017 gr-qc astro-ph.HE arXiv:1706.01812v1We describe the observation of GW170104, a gravitational-wave signal produced by the coalescence of a pair of stellar-mass black holes. The signal was measured on January 4, 2017 at 10:11:58.6 UTC by the twin advanced detectors of the Laser Interferometer Gravitational-Wave Observatory during their second observing run, with a network signal-to-noise ratio of 13 and a false alarm rate less than 1 in 70,000 years. The inferred component black hole masses are $31.2^{+8.4}_{-6.0}\,M_\odot$ and $19.4^{+5.3}_{-5.9}\,M_\odot$ (at the 90% credible level). The black hole spins are best constrained through measurement of the effective inspiral spin parameter, a mass-weighted combination of the spin components perpendicular to the orbital plane, $\chi_\mathrm{eff} = -0.12^{+0.21}_{-0.30}.$ This result implies that spin configurations with both component spins positively aligned with the orbital angular momentum are disfavored. The source luminosity distance is $880^{+450}_{-390}~\mathrm{Mpc}$ corresponding to a redshift of $z = 0.18^{+0.08}_{-0.07}$. We constrain the magnitude of modifications to the gravitational-wave dispersion relation and perform null tests of general relativity. Assuming that gravitons are dispersed in vacuum like massive particles, we bound the graviton mass to $m_g \le 7.7 \times 10^{-23}~\mathrm{eV}/c^2$. In all cases, we find that GW170104 is consistent with general relativity.
- Apr 18 2017 gr-qc arXiv:1704.04628v4During their first observational run, the two Advanced LIGO detectors attained an unprecedented sensitivity, resulting in the first direct detections of gravitational-wave signals and GW151226, produced by stellar-mass binary black hole systems. This paper reports on an all-sky search for gravitational waves (GWs) from merging intermediate mass black hole binaries (IMBHBs). The combined results from two independent search techniques were used in this study: the first employs a matched-filter algorithm that uses a bank of filters covering the GW signal parameter space, while the second is a generic search for GW transients (bursts). No GWs from IMBHBs were detected, therefore, we constrain the rate of several classes of IMBHB mergers. The most stringent limit is obtained for black holes of individual mass $100\,M_\odot$, with spins aligned with the binary orbital angular momentum. For such systems, the merger rate is constrained to be less than $0.93~\mathrm{Gpc^{-3}\,yr}^{-1}$ in comoving units at the $90\%$ confidence level, an improvement of nearly 2 orders of magnitude over previous upper limits.
- Apr 13 2017 gr-qc arXiv:1704.03719v3Results are presented from a semi-coherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run (O1). The search combines a frequency domain matched filter (Bessel-weighted $\mathcal{F}$-statistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60-650 Hz. Frequentist 95% confidence strain upper limits, $h_0^{95\%} = 4.0\times10^{-25}$, $8.3\times10^{-25}$, and $3.0\times10^{-25}$ for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are $\leq 10$ times higher than the theoretical torque-balance limit at 106 Hz.
- Jan 27 2017 astro-ph.HE gr-qc arXiv:1701.07709v5We present the result of searches for gravitational waves from 200 pulsars using data from the first observing run of the Advanced LIGO detectors. We find no significant evidence for a gravitational-wave signal from any of these pulsars, but we are able to set the most constraining upper limits yet on their gravitational-wave amplitudes and ellipticities. For eight of these pulsars, our upper limits give bounds that are improvements over the indirect spin-down limit values. For another 32, we are within a factor of 10 of the spin-down limit, and it is likely that some of these will be reachable in future runs of the advanced detector. Taken as a whole, these new results improve on previous limits by more than a factor of two.
- We employ gravitational-wave radiometry to map the gravitational waves stochastic background expected from a variety of contributing mechanisms and test the assumption of isotropy using data from Advanced LIGO's first observing run. We also search for persistent gravitational waves from point sources with only minimal assumptions over the 20 - 1726 Hz frequency band. Finding no evidence of gravitational waves from either point sources or a stochastic background, we set limits at 90% confidence. For broadband point sources, we report upper limits on the gravitational wave energy flux per unit frequency in the range $F_{\alpha,\Theta}(f) < (0.1 - 56) \times 10^{-8}$ erg cm$^{-2}$ s$^{-1}$ Hz$^{-1}$ (f/25 Hz)$^{\alpha-1}$ depending on the sky location $\Theta$ and the spectral power index $\alpha$. For extended sources, we report upper limits on the fractional gravitational wave energy density required to close the Universe of $\Omega(f,\Theta) < (0.39-7.6) \times 10^{-8}$ sr$^{-1}$ (f/25 Hz)$^\alpha$ depending on $\Theta$ and $\alpha$. Directed searches for narrowband gravitational waves from astrophysically interesting objects (Scorpius X-1, Supernova 1987 A, and the Galactic Center) yield median frequency-dependent limits on strain amplitude of $h_0 <$ (6.7, 5.5, and 7.0) $\times 10^{-25}$ respectively, at the most sensitive detector frequencies between 130 - 175 Hz. This represents a mean improvement of a factor of 2 across the band compared to previous searches of this kind for these sky locations, considering the different quantities of strain constrained in each case.
- A wide variety of astrophysical and cosmological sources are expected to contribute to a stochastic gravitational-wave background. Following the observations of GW150914 and GW151226, the rate and mass of coalescing binary black holes appear to be greater than many previous expectations. As a result, the stochastic background from unresolved compact binary coalescences is expected to be particularly loud. We perform a search for the isotropic stochastic gravitational-wave background using data from Advanced LIGO's first observing run. The data display no evidence of a stochastic gravitational-wave signal. We constrain the dimensionless energy density of gravitational waves to be $\Omega_0<1.7\times 10^{-7}$ with 95% confidence, assuming a flat energy density spectrum in the most sensitive part of the LIGO band (20-86 Hz). This is a factor of ~33 times more sensitive than previous measurements. We also constrain arbitrary power-law spectra. Finally, we investigate the implications of this search for the background of binary black holes using an astrophysical model for the background.
- Nov 24 2016 gr-qc astro-ph.HE arXiv:1611.07531v2Parameter estimates of GW150914 were obtained using Bayesian inference, based on three semi-analytic waveform models for binary black hole coalescences. These waveform models differ from each other in their treatment of black hole spins, and all three models make some simplifying assumptions, notably to neglect sub-dominant waveform harmonic modes and orbital eccentricity. Furthermore, while the models are calibrated to agree with waveforms obtained by full numerical solutions of Einstein's equations, any such calibration is accurate only to some non-zero tolerance and is limited by the accuracy of the underlying phenomenology, availability, quality, and parameter-space coverage of numerical simulations. This paper complements the original analyses of GW150914 with an investigation of the effects of possible systematic errors in the waveform models on estimates of its source parameters. To test for systematic errors we repeat the original Bayesian analyses on mock signals from numerical simulations of a series of binary configurations with parameters similar to those found for GW150914. Overall, we find no evidence for a systematic bias relative to the statistical error of the original parameter recovery of GW150914 due to modeling approximations or modeling inaccuracies. However, parameter biases are found to occur for some configurations disfavored by the data of GW150914: for binaries inclined edge-on to the detector over a small range of choices of polarization angles, and also for eccentricities greater than $\sim$0.05. For signals with higher signal-to-noise ratio than GW150914, or in other regions of the binary parameter space (lower masses, larger mass ratios, or higher spins), we expect that systematic errors in current waveform models may impact gravitational-wave measurements, making more accurate models desirable for future observations.
- Nov 24 2016 astro-ph.HE gr-qc arXiv:1611.07947v3We present the results of the search for gravitational waves (GWs) associated with $\gamma$-ray bursts detected during the first observing run of the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO). We find no evidence of a GW signal for any of the 41 $\gamma$-ray bursts for which LIGO data are available with sufficient duration. For all $\gamma$-ray bursts, we place lower bounds on the distance to the source using the optimistic assumption that GWs with an energy of $10^{-2}M_\odot c^2$ were emitted within the $16$-$500\,$Hz band, and we find a median 90% confidence limit of 71$\,$Mpc at 150$\,$Hz. For the subset of 19 short/hard $\gamma$-ray bursts, we place lower bounds on distance with a median 90% confidence limit of 90$\,$Mpc for binary neutron star (BNS) coalescences, and 150 and 139$\,$Mpc for neutron star-black hole coalescences with spins aligned to the orbital angular momentum and in a generic configuration, respectively. These are the highest distance limits ever achieved by GW searches. We also discuss in detail the results of the search for GWs associated with GRB 150906B, an event that was localized by the InterPlanetary Network near the local galaxy NGC 3313, which is at a luminosity distance of 54$\,$Mpc ($z=0.0124$). Assuming the $\gamma$-ray emission is beamed with a jet half-opening angle $\leq 30^{\circ}$, we exclude a BNS and a neutron star-black hole in NGC 3313 as the progenitor of this event with confidence $>99$%. Further, we exclude such progenitors up to a distance of 102$\,$Mpc and 170$\,$Mpc, respectively.
- Nov 10 2016 gr-qc astro-ph.HE arXiv:1611.02972v1We present the results from an all-sky search for short-duration gravitational waves in the data of the first run of the Advanced LIGO detectors between September 2015 and January 2016. The search algorithms use minimal assumptions on the signal morphology, so they are sensitive to a wide range of sources emitting gravitational waves. The analyses target transient signals with duration ranging from milliseconds to seconds over the frequency band of 32 to 4096 Hz. The first observed gravitational-wave event, GW150914, has been detected with high confidence in this search; other known gravitational-wave events fall below the search's sensitivity. Besides GW150914, all of the search results are consistent with the expected rate of accidental noise coincidences. Finally, we estimate rate-density limits for a broad range of non-BBH transient gravitational-wave sources as a function of their gravitational radiation emission energy and their characteristic frequency. These rate-density upper-limits are stricter than those previously published by an order-of-magnitude.
- We report here the non-detection of gravitational waves from the merger of binary neutron star systems and neutron-star--black-hole systems during the first observing run of Advanced LIGO. In particular we searched for gravitational wave signals from binary neutron star systems with component masses $\in [1,3] M_{\odot}$ and component dimensionless spins $< 0.05$. We also searched for neutron-star--black-hole systems with the same neutron star parameters, black hole mass $\in [2,99] M_{\odot}$ and no restriction on the black hole spin magnitude. We assess the sensitivity of the two LIGO detectors to these systems, and find that they could have detected the merger of binary neutron star systems with component mass distributions of $1.35\pm0.13 M_{\odot}$ at a volume-weighted average distance of $\sim$ 70Mpc, and for neutron-star--black-hole systems with neutron star masses of $1.4M_\odot$ and black hole masses of at least $5M_\odot$, a volume-weighted average distance of at least $\sim$ 110Mpc. From this we constrain with 90% confidence the merger rate to be less than 12,600 Gpc$^{-3}$yr$^{-1}$ for binary-neutron star systems and less than 3,600 Gpc$^{-3}$yr$^{-1}$ for neutron-star--black-hole systems. We find that if no detection of neutron-star binary mergers is made in the next two Advanced LIGO and Advanced Virgo observing runs we would place significant constraints on the merger rates. Finally, assuming a rate of $10^{+20}_{-7}$Gpc$^{-3}$yr$^{-1}$ short gamma ray bursts beamed towards the Earth and assuming that all short gamma-ray bursts have binary-neutron-star (neutron-star--black-hole) progenitors we can use our 90% confidence rate upper limits to constrain the beaming angle of the gamma-ray burst to be greater than ${2.3^{+1.7}_{-1.1}}^{\circ}$ (${4.3^{+3.1}_{-1.9}}^{\circ}$).
- Jul 11 2016 gr-qc astro-ph.HE arXiv:1607.02216v1We describe a directed search for continuous gravitational waves in data from the sixth LIGO science run. The target was the nearby globular cluster NGC 6544 at a distance of 2.7 kpc. The search covered a broad band of frequencies along with first and second frequency derivatives for a fixed sky position. The search coherently integrated data from the two LIGO interferometers over a time span of 9.2 days using the matched-filtering F-statistic. We found no gravitational-wave signals and set 95% confidence upper limits as stringent as 6.0 X 10^-25 on intrinsic strain and 8.5 X 10^-6 on fiducial ellipticity. These values beat the indirect limits from energy conservation for stars with characteristic spindown ages older than 300 years and are within the range of theoretical predictions for possible neutron-star ellipticities. An important feature of this search was use of a barycentric resampling algorithm which substantially reduced computational cost; this method will be used extensively in searches of Advanced LIGO and Virgo detector data.
- Jun 16 2016 gr-qc astro-ph.CO arXiv:1606.04856v3The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary black hole merger signals with total masses up to $100 M_\odot$ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than $5\sigma$ over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, and with an 87% probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range $9-240 \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.
- We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, accounting for all the spin-weighted quadrupolar modes, and separately accounting for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported in LVC_PE[1] (at 90% confidence), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Followup simulations performed using previously-estimated binary parameters most resemble the data. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz ∈[64 - 82M_⊙], mass ratio q = m2/m1 ∈[0.6,1], and effective aligned spin \chi_eff ∈[-0.3, 0.2], where \chi_eff = (S1/m1 + S2/m2) ⋅\hatL /M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and \chi_eff are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z between 64.0 - 73.5M_⊙and the final black hole's dimensionless spin parameter is consistent with af = 0.62 - 0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to LVC_PE[1].
- Jun 06 2016 gr-qc astro-ph.HE arXiv:1606.01210v1This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) on September 14, 2015 [1]. Reference presented parameter estimation [2] of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and a 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [2], and we quote updated component masses of $35^{+5}_{-3}\mathrm{M}_\odot$ and $30^{+3}_{-4}\mathrm{M}_\odot$ (where errors correspond to 90% symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate $0.65$ and a secondary spin estimate $0.75$ at 90% probability. Reference [2] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.
- May 12 2016 gr-qc astro-ph.IM arXiv:1605.03233v2We report on a comprehensive all-sky search for periodic gravitational waves in the frequency band 100-1500 Hz and with a frequency time derivative in the range of $[-1.18, +1.00]\times 10^{-8}$ Hz/s. Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from the Initial LIGO sixth science run and covers a larger parameter space with respect to any past search. A Loosely Coherent detection pipeline was applied to follow up weak outliers in both Gaussian (95% recovery rate) and non-Gaussian (75% recovery rate) bands. No gravitational wave signals were observed, and upper limits were placed on their strength. Our smallest upper limit on worst-case (linearly polarized) strain amplitude $h_0$ is ${9.7}\times 10^{-25}$ near 169 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of ${5.5}\times 10^{-24}$. Both cases refer to all sky locations and entire range of frequency derivative values.
- May 09 2016 gr-qc astro-ph.HE arXiv:1605.01785v2We present results from a search for gravitational-wave bursts coincident with a set of two core-collapse supernovae observed between 2007 and 2011. We employ data from the Laser Interferometer Gravitational-wave Observatory (LIGO), the Virgo gravitational-wave observatory, and the GEO 600 gravitational-wave observatory. The targeted core-collapse supernovae were selected on the basis of (1) proximity (within approximately 15 Mpc), (2) tightness of observational constraints on the time of core collapse that defines the gravitational-wave search window, and (3) coincident operation of at least two interferometers at the time of core collapse. We find no plausible gravitational-wave candidates. We present the probability of detecting signals from both astrophysically well-motivated and more speculative gravitational-wave emission mechanisms as a function of distance from Earth, and discuss the implications for the detection of gravitational waves from core-collapse supernovae by the upgraded Advanced LIGO and Virgo detectors.
- Apr 28 2016 astro-ph.HE gr-qc arXiv:1604.07864v3This Supplement provides supporting material for arXiv:1602.08492 . We briefly summarize past electromagnetic (EM) follow-up efforts as well as the organization and policy of the current EM follow-up program. We compare the four probability sky maps produced for the gravitational-wave transient GW150914, and provide additional details of the EM follow-up observations that were performed in the different bands.
- Mar 01 2016 astro-ph.HE gr-qc arXiv:1602.08492v4A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams.
- In Advanced LIGO, detection and astrophysical source parameter estimation of the binary black hole merger GW150914 requires a calibrated estimate of the gravitational-wave strain sensed by the detectors. Producing an estimate from each detector's differential arm length control loop readout signals requires applying time domain filters, which are designed from a frequency domain model of the detector's gravitational-wave response. The gravitational-wave response model is determined by the detector's opto-mechanical response and the properties of its feedback control system. The measurements used to validate the model and characterize its uncertainty are derived primarily from a dedicated photon radiation pressure actuator, with cross-checks provided by optical and radio frequency references. We describe how the gravitational-wave readout signal is calibrated into equivalent gravitational-wave-induced strain and how the statistical uncertainties and systematic errors are assessed. Detector data collected over 38 calendar days, from September 12 to October 20, 2015, contain the event GW150914 and approximately 16 of coincident data used to estimate the event false alarm probability. The calibration uncertainty is less than 10% in magnitude and 10 degrees in phase across the relevant frequency band 20 Hz to 1 kHz.
- Feb 12 2016 gr-qc astro-ph.HE arXiv:1602.03840v2On September 14, 2015, the Laser Interferometer Gravitational-wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be $<0.7$ (at 90% probability). The luminosity distance to the source is $410^{+160}_{-180}$ Mpc, corresponding to a redshift $0.09^{+0.03}_{-0.04}$ assuming standard cosmology. The source location is constrained to an annulus section of $610$ deg$^2$, primarily in the southern hemisphere. The binary merges into a black hole of $62^{+4}_{-4} M_\odot$ and spin $0.67^{+0.05}_{-0.07}$. This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.
- On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) simultaneously observed the binary black hole merger GW150914. We report the results of a matched-filter search using relativistic models of compact-object binaries that recovered GW150914 as the most significant event during the coincident observations between the two LIGO detectors from September 12 to October 20, 2015. GW150914 was observed with a matched filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 \sigma.
- Feb 12 2016 astro-ph.HE gr-qc arXiv:1602.03842v3A transient gravitational-wave signal, GW150914, was identified in the twin Advanced LIGO detectors on September 14, 2015 at 09:50:45 UTC. To assess the implications of this discovery, the detectors remained in operation with unchanged configurations over a period of 39 d around the time of the signal. At the detection statistic threshold corresponding to that observed for GW150914, our search of the 16 days of simultaneous two-detector observational data is estimated to have a false alarm rate (FAR) of $< 4.9 \times 10^{-6} \, \mathrm{yr}^{-1}$, yielding a $p$-value for GW150914 of $< 2 \times 10^{-7}$. Parameter estimation followup on this trigger identifies its source as a binary black hole (BBH) merger with component masses $(m_1, m_2) = \left(36^{+5}_{-4},29^{+4}_{-4}\right) \, M_\odot$ at redshift $z = 0.09^{+0.03}_{-0.04}$ (median and 90\% credible range). Here we report on the constraints these observations place on the rate of BBH coalescences. Considering only GW150914, assuming that all BBHs in the Universe have the same masses and spins as this event, imposing a search FAR threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of merger rates between $2$--$53 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ (comoving frame). Incorporating all search triggers that pass a much lower threshold while accounting for the uncertainty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from $13$--$600 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ depending on assumptions about the BBH mass distribution. All together, our various rate estimates fall in the conservative range $2$--$600 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$.
- We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10 - 500 s in a frequency band of 40 - 1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between $3.4 \times 10^{-5}$ - $9.4 \times 10^{-4}$ Mpc$^{-3}$ yr$^{-1}$ at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves.
- In this paper we present the results of the first low frequency all-sky search of continuous gravitational wave signals conducted on Virgo VSR2 and VSR4 data. The search covered the full sky, a frequency range between 20 Hz and 128 Hz with a range of spin-down between $-1.0 \times 10^{-10}$ Hz/s and $+1.5 \times 10^{-11}$ Hz/s, and was based on a hierarchical approach. The starting point was a set of short Fast Fourier Transforms (FFT), of length 8192 seconds, built from the calibrated strain data. Aggressive data cleaning, both in the time and frequency domains, has been done in order to remove, as much as possible, the effect of disturbances of instrumental origin. On each dataset a number of candidates has been selected, using the FrequencyHough transform in an incoherent step. Only coincident candidates among VSR2 and VSR4 have been examined in order to strongly reduce the false alarm probability, and the most significant candidates have been selected. The criteria we have used for candidate selection and for the coincidence step greatly reduce the harmful effect of large instrumental artifacts. Selected candidates have been subject to a follow-up by constructing a new set of longer FFTs followed by a further incoherent analysis. No evidence for continuous gravitational wave signals was found, therefore we have set a population-based joint VSR2-VSR4 90$\%$ confidence level upper limit on the dimensionless gravitational wave strain in the frequency range between 20 Hz and 128 Hz. This is the first all-sky search for continuous gravitational waves conducted at frequencies below 50 Hz. We set upper limits in the range between about $10^{-24}$ and $2\times 10^{-23}$ at most frequencies. Our upper limits on signal strain show an improvement of up to a factor of $\sim$2 with respect to the results of previous all-sky searches at frequencies below $80~\mathrm{Hz}$.
- Oct 14 2015 gr-qc astro-ph.HE arXiv:1510.03474v2We report results of a wideband search for periodic gravitational waves from isolated neutron stars within the Orion spur towards both the inner and outer regions of our Galaxy. As gravitational waves interact very weakly with matter, the search is unimpeded by dust and concentrations of stars. One search disk (A) is $6.87^\circ$ in diameter and centered on $20^\textrm{h}10^\textrm{m}54.71^\textrm{s}+33^\circ33'25.29"$, and the other (B) is $7.45^\circ$ in diameter and centered on $8^\textrm{h}35^\textrm{m}20.61^\textrm{s}-46^\circ49'25.151"$. We explored the frequency range of 50-1500 Hz and frequency derivative from $0$ to $-5\times 10^{-9}$ Hz/s. A multi-stage, loosely coherent search program allowed probing more deeply than before in these two regions, while increasing coherence length with every stage. Rigorous followup parameters have winnowed initial coincidence set to only 70 candidates, to be examined manually. None of those 70 candidates proved to be consistent with an isolated gravitational wave emitter, and 95% confidence level upper limits were placed on continuous-wave strain amplitudes. Near $169$ Hz we achieve our lowest 95% CL upper limit on worst-case linearly polarized strain amplitude $h_0$ of $6.3\times 10^{-25}$, while at the high end of our frequency range we achieve a worst-case upper limit of $3.4\times 10^{-24}$ for all polarizations and sky locations.
- To commemorate the 100th anniversary of general relativity, the International Society on General Relativity and Gravitation (ISGRG) commissioned a Centennial Volume, edited by the authors of this article. We jointly wrote introductions to the four Parts of the Volume which are collected here. Our goal is to provide a bird's eye view of the advances that have been made especially during the last 35 years, i.e., since the publication of volumes commemorating Einstein's 100th birthday. The article also serves as a brief preview of the 12 invited chapters that contain in-depth reviews of these advances. The volume will be published by Cambridge University Press and released in June 2015 at a Centennial conference sponsored by ISGRG and the Topical Group of Gravitation of the American Physical Society.
- Apr 03 2013 gr-qc astro-ph.HE arXiv:1304.0670v6We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are the most promising targets for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5-20 square degrees requires at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.
- Oct 15 2004 gr-qc arXiv:gr-qc/0410058v1The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian constraint, the failure of the delicate balance could lead to qualitatively wrong behavior rather than just decreased accuracy. This issue is different from instabilities caused by constraint-violating modes. Examples of stable numerical simulations of collapsing cosmological spacetimes exhibiting local mixmaster dynamics with and without Hamiltonian constraint enforcement are presented.
- Dec 23 2003 gr-qc arXiv:gr-qc/0312095v1Heuristic arguments and numerical simulations support the Belinskii et al (BKL) claim that the approach to the singularity in generic gravitational collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the dynamics of generic $T^2$-symmetric spacetime are presented.
- Jul 09 2002 gr-qc arXiv:gr-qc/0207035v1A systematic asymptotic expansion is developed for the gravitational wave degrees of freedom of a class of expanding, vacuum Gowdy cosmological spacetimes. In the wave map description of these models, the evolution of the gravitational wave amplitudes defines an orbit in the target space. The circumference of this orbit decays to zero indicating that the asymptotic spacetime is spatially homogeneous. A prescription is given to identify the asymptotic cosmological model for the gravitational wave degrees of freedom using the asymptotic point in the target space. The remaining metric function of the asymptotic cosmological model, found by solving the constraints, is determined by an effective energy of the gravitational waves rather than from the asymptotic point in the target space.
- Jan 18 2002 gr-qc arXiv:gr-qc/0201056v1This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
- Dec 10 2001 gr-qc arXiv:gr-qc/0112007v1Session A5 on numerical methods contained talks on colliding black holes, critical phenomena, investigation of singularities, and computer algebra.
- Jun 05 2001 gr-qc arXiv:gr-qc/0106009v1A combination of analytic and numerical methods has yielded a clear understanding of the approach to the singularity in spatially inhomogeneous cosmologies. Strong support is found for the longstanding claim by Belinskii, Khalatnikov, and Lifshitz that the collapse is dominated by local Kasner or Mixmaster behavior. The Method of Consistent Potentials is used to establish the consistency of asymptotic velocity term dominance (AVTD) (local Kasner behavior) in that no terms in Einstein's equations will grow exponentially when the VTD solution, obtained by neglecting all terms containing spatial derivatives, is substituted into the full equations. When the VTD solution is inconsistent, the exponential terms act dynamically as potentials either to drive the system into a consistent AVTD regime or to maintain an oscillatory approach to the singularity.
- Apr 17 2001 gr-qc arXiv:gr-qc/0104048v2We use qualitative arguments combined with numerical simulations to argue that, in the approach to the singularity in a vacuum solution of Einstein's equations with $T^2$ isometry, the evolution at a generic point in space is an endless succession of Kasner epochs, punctuated by bounces in which either a curvature term or a twist term becomes important in the evolution equations for a brief time. Both curvature bounces and twist bounces may be understood within the context of local mixmaster dynamics although the latter have never been seen before in spatially inhomogeneous cosmological spacetimes.
- Jan 16 2001 gr-qc arXiv:gr-qc/0101054v2A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.
- Jun 21 2000 gr-qc arXiv:gr-qc/0006071v1Previous studies \citeberger98a have provided strong support for a local, oscillatory approach to the singularity in U(1) symmetric, spatially inhomogeneous vacuum cosmologies on $T^3 \times R$. The description of a vacuum Bianchi type IX, spatially homogeneous Mixmaster cosmology (on $S^3 \times R$) in terms of the variables used to describe the U(1) symmetric cosmologies indicates that the oscillations in the latter are in fact those of local Mixmaster dynamics. One of the variables of the U(1) symmetric models increases only at the end of a Mixmaster era. Such an increase therefore yields a qualitative signature for local Mixmaster dynamics in spatially inhomogeneous cosmologies.
- Jan 27 2000 gr-qc arXiv:gr-qc/0001083v1By applying a standard solution generating technique, we transform an arbitrary vacuum Mixmaster solution on $S^3 \times {\bf R}$ to a new solution which is spatially inhomogeneous. We thereby obtain a family of exact, spatially inhomogeneous, vacuum spacetimes which exhibit Belinskii, Khalatnikov, and Lifshitz (BKL) oscillatory behavior. The solutions are constructed explicitly by performing the transformations on numerically generated, homogeneous Mixmaster solutions. Their behavior is found to be qualitatively like that seen in previous numerical simulations of generic U(1) symmetric cosmological spacetimes on $T^3 \times {\bf R}$.
- Jul 27 1999 gr-qc arXiv:gr-qc/9907083v1The method of consistent potentials is used to explain how a minimally coupled (classical) scalar field can suppress Mixmaster oscillations in the approach to the singularity of generic cosmological spacetimes.
- May 19 1998 gr-qc arXiv:gr-qc/9805063v1A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.
- May 01 1998 gr-qc arXiv:gr-qc/9804085v1A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.
- Jan 24 1998 gr-qc arXiv:gr-qc/9801078v1Numerical evidence supports the conjecture that polarized U(1) symmetric cosmologies have asymptotically velocity term dominated singularities.
- Jan 07 1998 gr-qc arXiv:gr-qc/9801010v1Spatially homogeneous but possibly anisotropic cosmologies have two main types of singularities: (1) asymptotically velocity term dominated (AVTD) - (reversing the time direction) the universe evolves to the singularity with fixed anisotropic collapse rates ; (2) Mixmaster-the anisotropic collapse rates change in a deterministicaly chaotic way. Much less is known about spatially inhomogeneous universes. It has been claimed that a generic universe would evolve toward the singularity as a different Mixmaster universe at each spatial point. I shall discuss how to predict whether a cosmology has an AVTD or Mixmaster singularity and whether or not our numerical simulations agree with these predictions.
- Dec 15 1997 gr-qc arXiv:gr-qc/9712055v3Numerical investigation of a class of inhomogeneous cosmological spacetimes shows evidence that at a generic point in space the evolution toward the initial singularity is asymptotically that of a spatially homogeneous spacetime with Mixmaster behavior. This supports a long-standing conjecture due to Belinskii et al. on the nature of the generic singularity in Einstein's equations.
- Oct 22 1997 gr-qc arXiv:gr-qc/9710102v1Numerical studies of the plane symmetric, vacuum Gowdy universe on $T^3 \times R$ yield strong support for the conjectured asymptotically velocity term dominated (AVTD) behavior of its evolution toward the singularity except, perhaps, at isolated spatial points. A generic solution is characterized by spiky features and apparent ``discontinuities'' in the wave amplitudes. It is shown that the nonlinear terms in the wave equations drive the system generically to the ``small velocity'' AVTD regime and that the spiky features are caused by the absence of these terms at isolated spatial points.
- Sep 29 1997 gr-qc arXiv:gr-qc/9709073v1The spatially homogeneous, isotropic Standard Cosmological Model appears to describe our Universe reasonably well. However, Einstein's equations allow a much larger class of cosmological solutions. Theorems originally due to Penrose and Hawking predict that all such models (assuming reasonable matter properties) will have an initial singularity. The nature of this singularity in generic cosmologies remains a major open question in general relativity. Spatially homogeneous but possibly anisotropic cosmologies have two types of singularities: (1) velocity dominated---(reversing the time direction) the universe evolves to the singularity with fixed anisotropic collapse rates ; (2) Mixmaster---the anisotropic collapse rates change in a deterministically chaotic way. Much less is known about spatially inhomogeneous universes. Belinskii, Khalatnikov, and Lifshitz (BKL) claimed long ago that a generic universe would evolve toward the singularity as a different Mixmaster universe at each spatial point. We shall report on the results of a program to test the BKL conjecture numerically. Results include a new algorithm to evolve homogeneous Mixmaster models, demonstration of velocity dominance and understanding of evolution toward velocity dominance in the plane symmetric Gowdy universes (spatial dependence in one direction), demonstration of velocity dominance in polarized U(1) symmetric cosmologies (spatial dependence in two directions), and exploration of departures from velocity dominance in generic U(1) universes.
- Aug 22 1997 gr-qc arXiv:gr-qc/9708050v1A standard and reasonable definition of asymptotic velocity term dominance (AVTD) shows that the numerical study by Hern and Stewart (gr-qc/9708038) confirms previous results that generic Gowdy cosmologies on $T^3 \times R$ have an AVTD singularity.
- Feb 05 1997 gr-qc arXiv:gr-qc/9702007v1We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$ spacelike surfaces.
- Oct 01 1996 gr-qc arXiv:gr-qc/9609072v1We present a new numerical algorithm for evolving the Mixmaster spacetimes. By using symplectic integration techniques to take advantage of the exact Taub solution for the scattering between asymptotic Kasner regimes, we evolve these spacetimes with higher accuracy using much larger time steps than previously possible. The longer Mixmaster evolution thus allowed enables detailed comparison with the Belinskii, Khalatnikov, Lifshitz (BKL) approximate Mixmaster dynamics. In particular, we show that errors between the BKL prediction and the measured parameters early in the simulation can be eliminated by relaxing the BKL assumptions to yield an improved map. The improved map has different predictions for vacuum Bianchi Type IX and magnetic Bianchi Type VI$_0$ Mixmaster models which are clearly matched in the simulation.
- Dec 05 1995 gr-qc arXiv:gr-qc/9512004v1We describe a numerical approach to address the BKL conjecture that the generic cosmological singularity is locally Mixmaster-like. We consider application of a symplectic PDE solver to three models of increasing complexity--spatially homogeneous (vacuum) Mixmaster cosmologies where we compare the symplectic ODE solver to a Runge-Kutta one, the (plane symmetric, vacuum) Gowdy universe on $T^3 \times R$ whose dynamical degrees of freedom satisfy nonlinearly coupled PDE's in one spatial dimension and time, and U(1) symmetric, vacuum cosmologies on $T^3 \times R$ which are the simplest spatially inhomogeneous universes in which local Mixmaster dynamics is allowed.
- Dec 05 1995 gr-qc arXiv:gr-qc/9512005v1Description of the magnetic Bianchi VI$_0$ cosmologies of LeBlanc, Kerr, and Wainwright in the formalisms both of Belinskii, Khalatnikov, and Lifshitz, and of Misner allows qualitative understanding of the Mixmaster-like singularity in those models.
- Dec 04 1995 gr-qc arXiv:gr-qc/9512003v1Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmololgies are discussed.
- May 31 1994 gr-qc arXiv:gr-qc/9405069v1We propose to study the behavior of complicated numerical solutions to Einstein's equations for generic cosmologies by following the geodesic motion of a swarm of test particles. As an example, we consider a cylinder of test particles initially at rest in the plane symmetric Gowdy universe on $T^3 \times R$. For a circle of test particles in the symmetry plane, the geodesic equations predict evolution of the circle into distortions and rotations of an ellipse as well as motion perpendicular to the plane. The evolutionary sequence of ellipses depends on the initial position of the circle of particles. We display snapshots of the evolution of the cylinder.
- Apr 07 1994 gr-qc arXiv:gr-qc/9404005v2In this paper we study space-times which evolve out of Cauchy data $(\Sigma,{}^3g,K)$ invariant under the action of a two-dimensional commutative Lie group. Moreover $(\Sigma,{}^3g,K)$ are assumed to satisfy certain completeness and asymptotic flatness conditions in spacelike directions. We show that asymptotic flatness and energy conditions exclude all topologies and group actions except for a cylindrically symmetric $R^3$, or a periodic identification thereof along the $z$-axis. We prove that asymptotic flatness, energy conditions and cylindrical symmetry exclude the existence of compact trapped surfaces. Finally we show that the recent results of Christodoulou and Tahvildar-Zadeh concerning global existence of a class of wave-maps imply that strong cosmic censorship holds in the class of asymptotically flat cylindrically symmetric electro-vacuum space-times.
- Aug 18 1993 gr-qc arXiv:gr-qc/9308016v1To assess the validity of the Belinskii, Khalatnikov, and Lifshitz (BKL) approximation to Mixmaster dynamics, it would be useful to evaluate the BKL discrete parameters as a byproduct of the numerical solution of Einstein's equations. An algorithm to do this and results for a typical trajectory are presented.
- Jul 24 1993 gr-qc arXiv:gr-qc/9307032v1Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits naturally into the Einstein equations for a large class of cosmological models and thus allows study of their approach to the singularity. The numerical method also naturally singles out the asymptotically velocity term dominated (AVTD) behavior known to be characteristic of some of these models, conjectured to describe others, and probably characteristic of a subclass of the rest. The method is first applied to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions are used as a code test and demonstrate that a 4th order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geodesic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforwardly generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one spacelike U(1) symmetry.