In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem, or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. It was recently pointed out that such near-horizon structures can lead to late-time echoes in the black hole merger gravitational wave signals that are otherwise indistinguishable from GR. We search for observational signatures of these echoes in the gravitational wave data released by advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), following the three black hole merger events GW150914, GW151226, and LVT151012. In particular, we for repeating damped echoes with time-delays of $8 M \log M$ (+spin corrections, in Planck units), corresponding to Planck-scale departures from GR near their respective horizons. Accounting for the look elsewhere effect due to uncertainty in the echo template, we find tentative evidence for Planck-scale structure near black hole horizons at false detection probability of $1\%$ (corresponding to $2.5\sigma$ significance level). Future observations from interferometric detectors at higher sensitivity, along with more physical echo templates, will be able to confirm (or rule out) this finding, providing possible empirical evidence for alternatives to classical black holes, such as in ${\it firewall}$ or ${\it fuzzball}$ paradigms.
Gravitational wave echoes provide our most direct and surprising observational window into quantum nature of black holes. Three years ago, the first search for echoes from Planck-scale modifications of general relativity near black hole event horizons led to tentative evidence at false detection probability of 1\% arXiv:1612.00266 . The study introduced a naive phenomenological model and used the public data release by the Advanced LIGO gravitational wave observatory for the first observing run O1 (GW150914, GW151226, and LVT151012, now GW151012). Here, we provide a status update on various observational searches for echoes by independent groups, and argue that they can all be consistent if echoes are most prominent at lower frequencies and/or in binary mergers of more extreme mass ratio. We also point out that the only reported "detection" of echoes (with $>4σ$ confidence) at 1.0 second after the binary neutron star merger GW170817 arXiv:1803.10454 is coincident with the formation time of the black hole inferred from electromagnetic observations.
Being arguably the most massive binary black hole merger event observed to date, GW190521 deserves special attention. The exceptionally loud ringdown of this merger makes it an ideal candidate to search for gravitational wave echoes, a proposed smoking gun for the quantum structure of black hole horizons. We perform a multipronged search for echoes via two well-established and independent pipelines; a template-based search for stimulated emission of Hawking radiation, or Boltzmann echoes, and the model-agnostic coherent WaveBurst (cwb) search. Stimulated Hawking radiation from the merger is proposed to lead to postmerger echoes at horizon mode frequency of $\ensuremath{\sim}50\text{ }\text{ }\mathrm{Hz}$ (for quadrupolar gravitational radiation), repeating at intervals of $\ensuremath{\sim}1$ second, due to partial reflection off Planckian quantum structure of the horizon. An analysis using dynamic nested sampling yields a Bayesian evidence of ${8}_{\ensuremath{-}2}^{+4}$ (90% confidence level) for this signal following GW190521, carrying an excess of ${6}_{\ensuremath{-}5}^{+10}%$ in gravitational wave energy, relative to the main event (consistent with the predicted amplitude of Boltzmann echoes). The ``look-elsewhere'' effect is estimated by using general relativity (plus Boltzmann echoes) injections in real data, before and after the event, giving a false (true) positive detection probability for higher Bayes factors of ${1.5}_{\ensuremath{-}0.9}^{+1.2}%$ ($35\ifmmode\pm\else\textpm\fi{}7%$). Similarly, the reconstructed waveform of the first echo in cwb carries an energy excess of ${13}_{\ensuremath{-}7}^{+16}%$. While the current evidence for stimulated Hawking radiation does not reach the gold standard of $5\ensuremath{\sigma}$ (or p-value $<3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$), our findings are in line with predictions for stimulated Hawking radiation at current detector sensitivities. The next generation of gravitational wave observatories can thus draw a definitive conclusion on the quantum nature of black hole horizons.
We consider the corrections due to quantum fluctuations of fields on charged black holes induced from the energy-momentum trace anomaly. Although the number of horizons stays unchanged and their positions receive only finite corrections, the geometry, thermodynamics and formation of RN black holes change seriously in particular for small ones. The entropy receives a logarithmic correction. The line $Q=M$, separating naked singularities from physical solutions is corrected, putting a lower limit on the mass and an upper limit on the temperature of the black hole as a function of its charge. The modifications are highly significant in the cases of near-extremal and small black holes. We also show that for black holes with small mass can stay in thermal equilibrium without any constraint on the volume of the container. This result is in contrast to the large black holes that need a finite volume container for thermal equilibrium. The minimum of the mass lower limits occurs at zero charge, resulting in the extremal Schwarzschild black hole with a specific mass of the order of $M_{p}$ and zero temperature. This state which has only gravitational interaction will be the final stage of Hawking radiation. Stability and lack of any interaction but gravitational, makes the extremal Schwarzschild black hole a serious candidate for dark matter particle.
The analysis of gravitational Wave (GW) data from advanced LIGO provides the mass of each companion of binary black holes as the source of GWs. The mass of events corresponding to the binary black holes from GW is above $20$ M$_\odot$ which is much larger than the mass of astrophysical black holes detected by x-ray observations. In this work, we examine primordial black holes (PBHs) as the source of LIGO events. Assuming that $100\%$ of the dark matter is made of PBHs, we estimate the rate at which these objects make binaries, merge, and produce GWs as a function of redshift. The gravitational lensing of GWs by PBHs can also enhance the amplitude of the strain. We simulate GWs sourced by binary PBHs, with the detection threshold of $S/N>10$ for both Livingston and Hanford detectors. For the log-normal mass function of PBHs, we generate the expected distribution of events, compare our results with the observed events, and find the best value of the mass function parameters (i.e., $M_c =25 M_\odot$ and $\sigma=0.6$) in the log-normal mass function. Comparing the expected number of events with the number of observed ones rules out the present-Universe binary formation PBH scenario as the candidate for the source of GW events detected by LIGO.
When two black holes merge, the late stage of gravitational wave emission is a superposition of exponentially damped sinusoids. According to the black hole no-hair theorem, this ringdown spectrum depends only on the mass and angular momentum of the final black hole. An observation of more than one ringdown mode can test this fundamental prediction of general relativity. Here we provide strong observational evidence for a multimode black hole ringdown spectrum using the gravitational wave event GW190521, with a Bayes factor of $\sim 40$ preferring two fundamental modes over one. The dominant mode is the $\ell=m=2$ harmonic, and the sub-dominant mode corresponds to the $\ell=m=3$ harmonic. We estimate the redshifted mass and dimensionless spin of the final black hole as $330^{+30}_{-40}\,\mathrm{M}_\odot$ and $0.87^{+0.05}_{-0.10}$, respectively. The detection of the two modes disfavors a binary progenitor with equal masses; the mass ratio is constrained to $0.4^{+0.2}_{-0.3}$. We find that the final black hole is consistent with the no hair theorem and constrain the fractional deviation from general relativity of the sub-dominant mode's frequency to be $-0.01^{+0.07}_{-0.11}$.
In recent publication (1612.00266), we demonstrated that the events in the first observing run of the Advanced LIGO gravitational wave observatory (aLIGO O1) showed tentative evidence for repeating from the abyss caused by Planck-scale structure near black hole horizons. By considering phenomenological echo model, we showed that the pure noise hypothesis is disfavored with p-value of 1%, i.e. higher amplitude for echoes than those in aLIGO O1 events are only recovered in 1% of random noise realizations. A recent preprint by Westerweck, et al. (1712.09966) provides careful re-evaluation of our analysis which claims a reduced statistical significance ... entirely consistent with noise. It is mystery to us why the authors make such statement, while they also find p-value of 2 $\pm$ 1% (given the Poisson error in their estimate) for the same model and dataset. This is p-erfectly consistent with our results, which would be commonly considered as disfavoring the null hypothesis, or moderate to significant evidence for echoes. Westerweck, et al. also point to diversity of the observed echo properties as evidence for statistical fluke, but such diversity is neither unique nor surprising for complex physical phenomena in nature.
When two black holes merge, the late stage of gravitational wave emission is a superposition of exponentially damped sinusoids. According to the black hole no-hair theorem, this ringdown spectrum depends only on the mass and angular momentum of the final black hole. An observation of more than one ringdown mode can test this fundamental prediction of general relativity. Here we provide strong observational evidence for a multimode black hole ringdown spectrum using the gravitational wave event GW190521, with a maximum Bayes factor of $56\pm1$ ($1\sigma$ uncertainty) preferring two fundamental modes over one. The dominant mode is the $\ell=m=2$ harmonic, and the sub-dominant mode corresponds to the $\ell=m=3$ harmonic. The amplitude of this mode relative to the dominant harmonic is estimated to be $A_{330}/A_{220} = 0.2^{+0.2}_{-0.1}$. We estimate the redshifted mass and dimensionless spin of the final black hole as $330_{-40}^{+30}~\mathrm{M}_{\odot}$ and $0.86_{-0.11}^{+0.06}$, respectively. We find that the final black hole is consistent with the no hair theorem and constrain the fractional deviation from general relativity of the sub-dominant mode's frequency to be $-0.01^{+0.08}_{-0.09}$.
We revisit the recent debate on the evidence for an overtone in the black hole ringdown of GW150914. By gating and inpainting the data, we discard the contamination from earlier parts of the gravitational wave signal before ringdown. This enables the parameter estimation to be conducted in the frequency domain, which is mathematically equivalent to the time domain method. We keep the settings as similar as possible to the previous studies by \textcite{Cotesta:2022pci} and Isi \textit{et al.}\cite{Isi:2019aib,Isi:2022mhy} which yielded conflicting results on the Bayes factor of the overtone. We examine the spectral contents of the matched-filtering in the frequency domain, and propose a convergence test to assess the validity of an overtone model. Our results find the Bayes factors for the overtone fall within $10$ and $26$ around a range of times centered at the best-fit merger time of GW150914, which supports the existence of an overtone in agreement with the conclusions of Isi \textit{et al.}\cite{Isi:2019aib,Isi:2022mhy}. Our work contributes to the understanding of how various methods affect the statistical significance of overtones.
Abstract A major aim of gravitational wave astronomy is to test observationally the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyse the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant (ℓ,m,n)=(3,3,0) ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability ∼0.02, which is consistent with a Bayes factor of 56±1 (1 σ uncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that only 1 in 250 simulated signals without a (3,3,0) mode yields a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable (3,3,0) mode they consistently yield a strong evidence and significant agnostic results. We also find that constraints on deviations from the (3,3,0) mode on GW190521-like signals with a (3,3,0) mode are consistent with what was obtained from our previous analysis of GW190521. Our results support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant (ℓ,m,n)=(3,3,0) mode.
'%3e%3cg id='e'%3e%3cg id='c' fill='none' stroke='%23fff' stroke-width='2'%3e%3cpath id='b' d='M0 1h26M1 10V5h8v4h8V5h-5M4 9h2m20 0h-5V5h8m0-5v9h8V0m-4 0v9' transform='scale(1.4)'/%3e%3cpath id='a' d='M0 7h9m1 0h9' transform='scale(2.8)'/%3e%3cuse xlink:href='%23a' y='120'/%3e%3cuse xlink:href='%23b' y='145.2'/%3e%3c/g%3e%3cg id='d'%3e%3cuse xlink:href='%23c' x='56'/%3e%3cuse xlink:href='%23c' x='112'/%3e%3cuse xlink:href='%23c' x='168'/%3e%3c/g%3e%3c/g%3e%3cuse xlink:href='%23d' x='168'/%3e%3cuse xlink:href='%23e' x='392'/%3e%3c/g%3e%3cg fill='%23da0000' transform='matrix(45 0 0 45 315 180)'%3e%3cg id='f'%3e%3cpath d='M-.548.836A.912.912 0 0 0 .329-.722 1 1 0 0 1-.548.836'/%3e%3cpath d='M.618.661A.764.764 0 0 0 .422-.74 1 1 0 0 1 .618.661M0 1l-.05-1L0-.787a.31.31 0 0 0 .118.099V-.1l-.04.993zM-.02-.85 0-.831a.144.144 0 0 0 .252-.137A.136.136 0 0 1 0-.925'/%3e%3c/g%3e%3cuse xlink:href='%23f' transform='scale(-1 1)'/%3e%3c/g%3e%3c/svg%3e)
