In the corpuscular picture of black hole there exists no geometric notion of horizon which, instead, only emerges in the semi-classical limit. Therefore, it is very natural to ask - what happens if we send a signal towards a corpuscular black hole? We show that quantum effects at the horizon scale imply the existence of a surface located at an effective radius $R=R_s(1+ε)$ slightly larger than the Schwarzschild radius $R_s,$ where $ε=1/N$ and $N$ is the number of gravitons composing the system. Consequently, the reflectivity of the object can be non-zero and, indeed, we find that incoming waves with energies comparable to the Hawking temperature can have a probability of backscattering of order one. Thus, modes can be trapped between the two potential barriers located at the photon sphere and at the surface of a corpuscular black hole, and periodic echoes can be produced. The time delay of echoes turns out to be of the same order of the scrambling time, i.e., in units of Planck length it reads $\sqrt{N}\,{\rm log}\,N.$ We also show that the $ε$-parameter, or in other words the compactness, of a corpuscular black hole coincides with the quantum coupling that measures the interaction strength among gravitons, and discuss the physical implications of this remarkable feature.
The total number of Hawking quanta emitted during the evaporation of a Schwarzschild black hole is proportional to the square of the initial mass or, equivalently, to the Bekenstein entropy. This simple, but little appreciated, fact is interpreted in terms of the recent discovery of black hole soft hair.
Exciting peculiarities of Planck-scale physics have immediate effects on the Bekenstein-Hawking radiation emitted from black holes (BHs). In this paper, using the tunneling formalism, we determine the Bekenstein-Hawking temperature for the vector particles from a backreacted black hole (BBH) constructed from a conformal scalar field surrounded by a BTZ (Banados-Teitelboim-Zanelli) BH. Then, under the effect of the generalized uncertainty principle, we extend our calculations for scalar particles to understand the effects of quantum gravity. Then, we calculate an evaporation time for the BBH, t…
We discuss an effective theory for the quantum static gravitational potential in spherical symmetry up to the first post-Newtonian correction. We build a suitable Lagrangian from the weak field limit of the Einstein-Hilbert action coupled to pressureless matter. Classical solutions of the field equation lead to the correct post-Newtonian expansion. Furthermore, we portray the Newtonian results in a quantum framework by means of a coherent quantum state, which is properly corrected to accomodate post-Newtonian corrections. These considerations provide a link between the corpuscular model of Dva…
Black holes in $d < 3$ spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose-Einstein condensates of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as $N_d \sim \left(L_d/\ell_{\rm …
We study the corpuscular model of an evaporating black hole consisting of a specific quantum state for a large number $N$ of self-confined bosons. The single-particle spectrum contains a discrete ground state of energy $m$ (corresponding to toy gravitons forming the black hole), and a gapless continuous spectrum (to accommodate for the Hawking radiation with energy $ω>m$). Each constituent is in a superposition of the ground state and a Planckian distribution at the expected Hawking temperature in the continuum. We first find that, assuming the Hawking radiation is the leading effect of the in…
We study echoes of free massless scalar from dyonic black holes in Einstein-Maxwell gravity extended with the quasi-topological electromagnetic term. These asymptotically-flat black holes all satisfy the dominant energy condition. We find that for suitable parameters, the effective potential can have double peaks and consequently echoes of quasinormal modes arise. In general the echo frequency associated with the initial wave packet released inside the two peaks is about twice the frequency of the one released outside.
A corpuscular quantum description of inflation shows that there is no fundamental problem with trans-Planckian excursions of the inflaton field up to about 100 Planck masses, with the upper bound coming from the corpuscular quantum effects. In this description the r-parameter measures the ratio of occupation numbers of gravitons versus inflatons, which, according to BICEP2, was roughly a half at the time of 60 e-foldings prior to the end of inflation. We stress that in non-Wilsonian UV self-completion of gravity any trans-Planckian mode coupled to inflaton is a black hole. Unlike the Wilsonian…
A classical black hole is characterized by a horizon that absorbs radiation of all frequencies incident on it. Perturbation of these black holes is well-understood via exponentially damped sinusoids known as quasi-normal modes. Any departure from such classical behavior near the horizon may induce significant modifications in the late time evolution of the perturbation leading to so-called gravitational wave echoes. This work considers the effect of black hole area-quantization on the formation of gravitational wave echoes. We investigate how the resulting echo waveform may depend on various m…
The holographic interpretation of the Randall-Sundrum model based on the adaptation of the AdS/CFT correspondence to the braneworld scenario states that the black holes localized on the brane are {\it quantum corrected}. This can be better understood from the fact that the classical $AdS_{5}$ bulk dynamics is dual to gravity coupled with CFT on the four dimensional brane. Based on the back reaction of the CFT on the classical black hole geometry, localized on the brane, it is expected that there exist possible near horizon modifications. This may result in the black hole horizon becoming parti…
We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static matter source from the weak field expansion of the Einstein-Hilbert action. By analysing a few classical solutions of the resulting field equation, we show that our construction leads to the expected post-Newtonian expressions. Next, we show that one can reproduce the classical Newtonian results very accurately by employing a coherent quantum state and modifi…
Echoes are known as modifications of the usual quasinormal ringing of a black hole at late times because of the deviation of space-time from the initial black-hole geometry in a small region near its event horizon. We consider a class of brane-world model solutions of the Shiromizu-Maeda-Sasaki equations, which describe both black holes and wormholes and interpolate between them via a continuous parameter. In this way the brane-world scenario provides a natural model for wormholes mimicking the black hole behavior if the continuous parameter is chosen near the threshold with a black-hole solut…
The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented compri…
It is often said that there is no gravity theory based on local action principles giving rise to firewall black hole solutions. Additionally, Guo and Mathur 2022 (2205.10921) have cast doubt on the observability of firewall echoes due to closed trapped surface produced by backreaction of macroscopic in-falling wave packets. In this paper, we bring Einstein-Maxwell-Dilaton action as a toy model that serves as counterexample to these assertions. Actions with Maxwell and dilaton fields emerge from several fundamental theories, such as the low energy limit of (super) string theory or Kaluza-Klein …
It is well known that a hypothetical compact object that looks like an Einsteinian (Schwarzschild or Kerr) black hole everywhere except a small region near its surface should have the ringdown profile predicted by the Einstein theory at early and intermediate times, but modified by the so-called echoes at late times. A similar phenomenon appears when one considers an Einsteinian black hole and a shell of matter placed at some distance from it, so that astrophysical estimates could be made for the allowed mass of the black hole environment. While echoes for both systems have been extensively st…
Gravitational wave echoes can be used as a significant observable to understand the properties of black holes horizon. In addition, echoes would also closely relate to the unique properties of compact objects. In this work we study the evolution of electromagnetic field and scalar field under the background of novel black-bounce spacetimes. Our results show an obvious echoes signal that can characterize the properties of novel black-bounce spacetimes, and a detailed analysis about the characteristics of the echoes signal is given. By studying the quasinormal ringdown of the three states of nov…
We try to shed some light on the role of matter in the final stages of black hole evaporation from the fundamental frameworks of classicalization and the black-to-white hole bouncing scenario. Despite being based on very different grounds, these two approaches attempt at going beyond the background field method and treat black holes as fully quantum systems rather than considering quantum field theory on the corresponding classical manifolds. They also lead to the common prediction that the semiclassical description of black hole evaporation should break down and the system be disrupted by int…
We consider a very simple model for gravitational wave echoes from black hole merger ringdowns which may arise from local Lorentz symmetry violations that modify graviton dispersion relations. If the corrections are sufficiently soft so they do not remove the horizon, the reflection of the infalling waves which trigger the echoes is very weak. As an example, we look at the dispersion relation of a test scalar field corrected by roton-like operators depending only on spatial momenta, in Gullstrand-Painlevé coordinates. The near-horizon regions of a black hole do become reflective, but only very…
Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detec…
The time evolution of the field perturbations in the wormhole and black bounce backgrounds are investigated. We find that the asymmetry of spacetime results in the asymmetry of the effective potential of the perturbed equation. The quasinormal modes are strongly dependent on the shapes of the effective potentials. Specifically, the signals of echoes arise in some wormhole cases and reflect the asymmetric properties of wormholes. We examine the features of echoes within different circumstances. Besides, the negative values of effective potentials usually imply the instability of the system. By …
In this work we argue that black hole area quantization of Bekenstein and Mukhanov should not give rise to measurable effects in terms of so-called gravitational wave echoes during black hole mergers. We outline that the quantum spectrum of a black hole should be washed out during and after black hole mergers, and hence one should not expect echoes in this scenario. The extreme broadening of the spectrum is due to the large particle emission rate during ringdown. Our results question key assumptions being made in recent literature on this topic.
Two seemingly distinct notions regarding black holes have captured the imagination of theoretical physicists over the past decade: First, black holes are conjectured to be fast scramblers of information, a notion that is further supported through connections to quantum chaos and decay of mutual information via AdS/CFT holography. Second, black hole information paradox has motivated exotic quantum structure near horizons of black holes (e.g., gravastars, fuzzballs, or firewalls) that may manifest themselves through delayed gravitational wave echoes in the aftermath of black hole formation or me…
One of the most triumphant predictions of the theory if general relativity was the recent LIGO-Virgo detection of gravitational wave (GW) signals produced in binary black hole (BH) mergers. However, it is suggested that exotic compact objects, proposed in quantum gravity models of BHs, may produce similar classical GW waveforms, followed by delayed repeating "echoes". In a companion paper [1], we have presented different arguments for a universal Boltzmann reflectivity of quantum BH horizons. Here, we investigate the resulting echoes from this prescription. We derive corresponding quasi-normal…
The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in f…
In present work, the evolution of scalar field and electromagnetic field under the background of the charged black-bounce spacetimes are investigated, and we obtain an obvious echoes signal which appropriately reports the properties of the charged black-bounce spacetimes and disclose the physical reasons behind such phenomena. Furthermore, by studying the quasinormal ringdown, we analyze the three states of the charged black-bounce spacetimes in detail, our results show that the echoes signal only appears when $(\rvert {Q}\rvert \le m)$ and $(\rvert {l}\rvert > m+ \sqrt{m ^{2}-Q^{2} })$ in thi…
Quantum nature of black hole horizons has been a subject of recent interest and scrutiny. In particular, a near-horizon quantum violation of the equivalence principle has been proposed as a resolution of the black hole information paradox. Such a violation may lead to a modified dispersion relation at high energies, which could become relevant due to the intense gravitational blueshift experienced by ingoing gravitational waves. We investigate the ringdown for a perturbed black hole with such a modified dispersion relation and find that infalling gravitational waves are partially reflected nea…
In the string theory, the fundamental blocks of nature are not particles but one-dimensional strings. Therefore, a generalization of this idea is to think of it as a cloud of strings. Rodrigues et al. embedded the black bounces spacetime into the string cloud, which demonstrates that the existence of the string cloud makes the Bardeen black hole singular, while the black bounces spacetime remains regular. On the other hand, the echoes are the correction to the late stage of the quasinormal ringing for a black hole, which is caused by the deviation of the spacetime relative to the initial black…
Influence of quantum decoherence on black hole shadow visibility and time domain echoes
College of Physics and Optoelectronic Engineering, Chongqing Normal University（重庆师范大学物理与电子工程学院）；School of Big Data and Artificial Intelligence, Fuyang University of Technology（阜阳工业大学大数据与人工智能学院）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Instituto de Física, Universidade de São Paulo（圣保罗大学物理研究所）；Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力国家实验室引力波实验中心）
Gravitational waves are rapidly becoming a very reliable tool for testing alternative theories of gravity. In particular, features in the gravitational wave emission during black hole ringdown phase provide a direct probe of the spacetime outside the black hole. In this article, we consider black holes in ghost-free massive gravity. These black holes generically have scalar hair. We found that a simple coupling between gravitational perturbations and this scalar hair can change the quasinormal ringing of the black hole, and in particular, produce echoes in the emitted gravitational waves. This…
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…
Recently the possibility of detecting echoes of ringdown gravitational waves from binary black hole mergers was shown. The presence of echoes is expected if the black hole is surrounded by a mirror that reflects gravitational waves near the horizon. Here, we present slightly more sophisticated templates motivated by a waveform which is obtained by solving the linear perturbation equation around a Kerr black hole with a complete reflecting boundary condition in the stationary traveling wave approximation. We estimate that the proposed template can bring about $10\%$ improvement in the signal-to…
In the context of higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, are more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, inherited from the projection of the higher dimensional Weyl tensor onto the four dimensional spacetime we live in. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact object…
We show that the higher order curvature corrections to general relativity in the strong gravity regime of near horizon scales produce a rapidly oscillating and infalling Ricci scalar fireball just outside the horizon. This can generate the ringdown modes of gravitational waves having the same natural frequency as those which are generated by the black hole mergers. Our analysis provides a viable explanation to the echoes in the ringdown modes recently detected from the LIGO data, without invoking the existence of any exotic structures at the horizon.
Gravitational-wave Echoes Beyond the Hubble Time from Quantum Black Holes
RIKEN iTHEMS（理化学研究所 iTHEMS）；Department of Physics, Kindai University（近畿大学物理系）；School of Engineering Science, Kochi University of Technology（高知工科大学工程科学学部）
The existence of exact solutions which represent a lattice of black holes at a scalar-field-dominated cosmological bounce suggests that black holes could persist through successive eras of a cyclic cosmology. Here we explore some remarkable cosmological consequences of this proposal. In different mass ranges pre-big-bang black holes could explain the dark matter, provide seeds for galaxies, generate entropy and even drive the bounce itself. The cycles end naturally when the filling factor of the black holes reaches unity and this could entail a dimensional transition.
Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal fre…
In a 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 "echoes from the abyss" caused by Planck-scale structure near black hole horizons. By considering a phenomenological echo model, we showed that the pure noise hypothesis is disfavored with a 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 a careful re-e…
We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the corpuscular picture of black holes.
Gravitational wave echoes from the black holes have been suggested as a crucial observable to probe the spacetime in the vicinity of the horizon. In particular, it was speculated that the echoes are closely connected with specific characteristics of the exotic compact objects, and moreover, possibly provide an access to the quantum nature of gravity. Recently, it was shown that the discontinuity in the black hole metric substantially modifies the asymptotical behavior of quasinormal frequencies. In the present study, we proceed further and argue that a discontinuity planted into the metric fur…
With the advent of gravitational wave astronomy, searching for gravitational wave echoes from black holes (BHs) is becoming an interesting probe of their quantum nature near their horizons. Newborn BHs may be strong emitters of echoes, as they accompany large perturbations in the surrounding spacetime upon formation. Utilizing the Quantum Black Hole Seismology framework (Oshita et al. 2020), we study the expected echoes upon BH formation resulting from neutron star mergers and failed supernovae. For BH remnants from neutron star mergers, we evaluate the consistency of these models with the rec…
Echoes and quasinormal modes of asymmetric black bounces
Universidade Federal do Ceará (UFC)（塞阿拉联邦大学）；Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（瓦伦西亚大学/西班牙国家研究委员会粒子物理研究所）；Programa de Pós-graduação em Física, Universidade Federal do Maranhão（马拉尼昂联邦大学）
New theoretical approaches developed in the last years predict that macroscopic quantum gravity effects in black holes should lead to modifications of the gravitational wave signals expected in the framework of classical general relativity, with these modifications being characterized by the existence of dampened repetitions of the primary signal. Here we use the fact that non-perturbative corrections to the near-horizon external geometry of black holes are necessary for these modifications to exist, in order to classify different proposals and paradigms with respect to this criterion and stud…
The existence of black hole horizons has not been strictly proven observationally, and indeed it may not be possible to do so. However, alternatives may be established by the observation of gravitational wave echoes that probe possible near-horizon structure. These echoes are proposed to be generated in exotic compact objects that are horizonless and feature a partially reflecting "wall" inside their light rings, creating a cavity in which gravitational perturbations may echo, while leaking out through the angular momentum barrier with each pass. The characteristic signature of echoes is a com…
We establish a connection between the ultra-Planckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a bound-state of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the tree-level N-graviton scattering S-matrix elements in a kinematical regime (called classicalization limit) where the two incoming ultra-Planckian grav…
Searches for gravitational wave echoes in the aftermath of mergers and/or formation of astrophysical black holes have recently opened a novel and surprising window into the quantum nature of their horizons. Similar to astro- and helioseismology, study of the spectrum of quantum black holes provides a promising method to understand their inner structure, what we call $\textit{quantum black hole seismology}$. We provide a detailed numerical and analytic description of this spectrum in terms of the properties of the Kerr spacetime and quantum black hole horizons, showing that it drastically diffe…
We study the waveforms of time signals produced by scalar perturbations in static hairy black holes, in which the perturbations can be governed by a double-peak effective potential. The inner potential peak would give rise to echoes, which provide a powerful tool to test the Kerr hypothesis. The waveforms are constructed in the time and frequency domains, and we find that the late-time waveforms are determined by the long-lived and sub-long-lived quasinormal modes, which are trapped in the potential valley and near the smaller peak, respectively. When the distance between the peaks is signific…
Here we propose a simple explanation why echoes from wormholes mimicking black holes may be so small that they cannot be observed. The essence of the effect is in the redistribution of the initial energy of gravitational wave among multiple universes, connected by a wormhole.
The first direct observation of a binary neutron star (BNS) merger was a watershed moment in multi-messenger astronomy. However, gravitational waves from GW170817 have only been observed prior to the BNS merger, but electromagnetic observations all follow the merger event. While post-merger gravitational wave signal in general relativity is too faint (given current detector sensitivities), here we present the first tentative detection of post-merger gravitational wave "echoes" from a highly spinning "black hole" remnant. The echoes may be expected in different models of quantum black holes tha…
Gravitational wave astronomy provides an unprecedented opportunity to test the nature of black holes and search for exotic, compact alternatives. Recent studies have shown that exotic compact objects (ECOs) can ring down in a manner similar to black holes, but can also produce a sequence of distinct pulses resembling the initial ringdown. These "echoes" would provide definite evidence for the existence of ECOs. In this work we study the generation of these echoes in a generic, parametrized model for the ECO, using Green's functions. We show how to reprocess radiation in the near-horizon region…
The recent detection of gravitational waves has generated interest in alternatives to the black hole interpretation of sources. One set of such alternatives involves a prediction of gravitational wave "echoes". We consider two aspects of possible echoes: First, general features of echoes coming from spacetime reflecting conditions. We find that the detailed nature of such echoes does not bear any clear relationship to quasi-normal frequencies. Second, we point out the pitfalls in the analysis of local reflecting "walls" near the horizon of rapidly rotating black holes.
