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 partially reflective, thus giving rise to echoes in the ringdown signal in gravitational wave observations. In this paper, we investigate the existence of such echoes in the ringdown phase of a black hole localized on the brane, carrying a \emph{negative} tidal charge, and establish the layout for future investigation of higher dimensional effects in the ringdown signal. Confirmed detections of echoes at the current levels of instrumental sensitivity can constrain the dimensionless value of tidal charge to $|Q| \lesssim M^2$ .
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 have studied the stability of wormhole geometries, under massless scalar, electromagnetic and axial gravitational perturbations, in the context of higher dimensional spacetimes. Intriguingly, the construction of a wormhole spacetime in the presence of higher dimensions, known as braneworld wormholes, \emph{does not} require the existence of exotic matter fields, unlike the scenario in four spacetime dimensions. Being a nonvacuum spacetime, the effective potential experienced by the axial gravitational perturbation differs considerably from the scenarios involving black holes. In particular,…
The thermodynamics and phase transitions of charged RN-AdS and rotating Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structur…
In this review, we summarize current understandings of black hole solutions in various braneworld models, including the Arkani-Hamed-Dimopoulos-Dvali model, the Randall-Sundrum (RS) models, the Karch-Randall (KR) model and the Dvali-Gabadadze-Porrati model. After illustrating basic properties of each braneworld model, we introduce the bulk/brane correspondence in the RS and KR braneworld models, adding supporting evidence for it. We then summarize the studies on braneworld black hole solutions, which consist of constructing exact or approximate solutions and investigating the phase diagram of …
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.
We derive the Lichnerowicz equation in the presence of the Gauss-Bonnet term. Using the modified Lichnerowicz equation we study the metric perturbations of Gauss-Bonnet black strings in Codimension-2 Braneworlds.
By using the quantum tunneling approach over semiclassical approximations, we study the quantum corrections to the Hawking temperature, entropy and Bekenstein-Hawking entropy-area relation for a black hole lying on a brane.
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…
This paper aims to evince the corrections on the black string warped horizon in the braneworld paradigm, and their drastic physical consequences, as well as to provide subsequent applications in astrophysics. Our analysis concerning black holes on the brane departs from the Schwarzschild case, where the black string is unstable to large-scale perturbation. The cognizable measurability of the black string horizon corrections due to braneworld effects is investigated, as well as their applications in the variation of quasars luminosity. We delve into the case wherein two solutions of Einstein's …
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…
We introduce two new families of solutions to the vacuum Einstein equations with negative cosmological constant in 5 dimensions. These solutions are static black holes whose horizons are modelled on the 3-geometries nilgeometry and solvegeometry. Thus the horizons (and the exterior spacetimes) can be foliated by compact 3-manifolds that are neither spherical, toroidal, hyperbolic, nor product manifolds, and therefore are of a topological type not previously encountered in black hole solutions. As an application, we use the solvegeometry solutions to construct Bianchi VI$_{-1}$ braneworld cosmo…
In the Randall-Sundrum two-brane model (RS1), a Kerr black hole on the brane can be naturally identified with a section of rotating black string. To estimate Kaluza-Klein (KK) corrections on gravitational waves emitted by perturbed rotating black strings, we give the effective Teukolsky equation on the brane which is separable equation and hence numerically manageable. In this process, we derive the master equation for the electric part of the Weyl tensor $E_{μν}$ which would be also useful to discuss the transition from black strings to localized black holes triggered by Gregory-Laflamme inst…
In this paper, we use the strong field limit approach to investigate the gravitational lensing properties of braneworld black holes. Applying this method to the supermassive black hole at the centre of our galaxy, the lensing observables for some candidate braneworld black hole metrics are compared with those for the standard Schwarzschild case. It is found that braneworld black holes could have significantly different observational signatures to the Schwarzschild black hole.
We present the first numerical study of the full dynamics of a braneworld scenario, working within the framework of the single brane model of Randall and Sundrum (RSII). In particular, we study the process of gravitational collapse driven by a massless scalar field which is confined to the brane. Imposing spherical symmetry on the brane, we show that the evolutions of sufficiently strong initial configurations of the scalar field result in black holes that have finite extension into the bulk. Furthermore, we find preliminary evidence that the black holes generated form a unique sequence, irres…
We examine the stability of extremal braneworld Reissner-Nordström black holes under massive charged scalar perturbations. We show that similar to the four-dimensional case, the superradiant amplification can occur in braneworld charged holes. More interestingly we find that when the spacetime dimension is higher than four, a trapping potential well can emerge outside the braneworld black hole. This potential well is the extra dimensional effect and does not exist in four dimensions. It triggers the superradiant instability of the extremal braneworld charged holes.
In this thesis we investigate black holes in the Randall-Sundrum braneworld scenario. We begin with an overview of extra-dimensional physics, from the original proposal of Kaluza and Klein up to the modern braneworld picture of extra dimensions. A detailed description of braneworld gravity is given, with particular emphasis on its compatibility with experimental tests of gravity. We then move on to a discussion of static, spherically symmetric braneworld black hole solutions. Assuming an equation of state for the ``Weyl term'', which encodes the effects of the extra dimension, we are able to c…
Recent study shows that the magnetic reconnection can serve as an efficient mechanism to extract energy from rapidly spinning black holes. In this paper, we consider the effects of the tidal charge on the energy extraction via the magnetic reconnection in the backgrounds of a spinning braneworld black hole. With the increase of the tidal charge, we find that both the energies of the accelerated plasma and decelerated plasma decrease for the observer located at infinity. To achieve the purpose extracting the net energy from the black hole, the decelerated plasma should take negative energy. The…
The braneworld description of our universe entails a large extra dimension and a fundamental scale of gravity that might be lower by several orders of magnitude compared to the Planck scale. An interesting consequence of the braneworld scenario is in the nature of spherically symmetric vacuum solutions to the brane gravitational field equations which could represent black holes with properties quite distinct compared to ordinary black holes in 4-dimensions. We discuss certain key features of some braneworld black hole geometries. Such black holes are likely to have diverse cosmological and ast…
We study the static, analytical solution of black holes in the warped DGP braneworld scenario. We show that the linearized field equations and matching conditions lead to solutions that are not compatible with Schwarzschild-(A)dS$_{(4)}$ solutions on the brane. This incompatibility is similar to vDVZ discontinuity in massive gravity theory. Following the standard procedure to remove this discontinuity, which firstly was proposed by Vainshtein, we keep some appropriate nonlinear terms in the field equations. This strategy has its origin in the fact that the spatial extrinsic curvature of the br…
We construct analogue black hole solutions in the braneworld scenario. The quantum fluctuations of condensate gravitons propagating around a $4+n$-dimensional gravitational potential are found yielding a metric similar to higher dimensional Schwarzschild black hole line-element. Black hole analogue solutions in Randall-Sundrum and Dvali-Gabadadze-Porrati brane world models are also constructed. The properties of such black hole analogues are discussed.
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…
Application of the adS/CFT correspondence to the RS models may predict that there is no static solution for black holes with a radius larger than the bulk curvature scale. When the black hole has an extremal horizon, however, the correspondence suggests that the black hole can stay static. We focus on the effects of cosmological constant on the brane on such extremal brane-localized black holes. We observe that the positive cosmological constant restrict the black hole size on the brane as in ordinary four-dimensional general relativity. The maximum black hole size differs from that in four-di…
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 …
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 wave…
Evaluating Kaluza-Klein (KK) corrections is indispensable to test the braneworld scenario. In this paper, we propose a novel symmetry approach to a 4-dimensional effective action with KK corrections for the Randall-Sundrum two-brane system. The result can be used to assess the validity of the low energy approximation. Also, our result provides the basis for predicting CMB spectrum with KK corrections and the study of the transition from black strings to black holes.
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…
We study gravitational waves in the black string Randall-Sundrum braneworld. We present a reasonably self-contained and complete derivation of the equations governing the evolution of gravitational perturbations in the presence of a brane localized source, and then specialize to the case of spherical radiation from a pointlike body in orbit around the black string. We solve for the resulting gravitational waveform numerically for a number of different orbital parameters.
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…
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…
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 …
We describe a concise general scheme for constructing solutions of Einstein-Maxwell-Kalb-Ramond gravity-matter system in bulk space-time interacting self-consistently with one or more (widely separated) codimension-one electrically charged lightlike branes. The lightlike brane dynamics is explicitly given by manifestly reparametrization invariant world-volume actions. We present several explicit classes of solutions with different physical interpretation as wormhole-like space-times with one, two or more "throats", singularity-free black holes, brane worlds and space-times undergoing a sequenc…
We look for spherically symmetric star or black hole solutions on a Randall-Sundrum brane from the perspective of the bulk. We take a known bulk solution, and analyse possible braneworld trajectories within it that correspond, from the braneworld point of view, to solutions of the brane Tolman-Oppenheimer-Volkoff equations. Our solutions are therefore embedded consistently into a full bulk solution. We find the full set of static gravitating matter sources on a brane in a range of bulk spacetimes, analyzing which can correspond to physically sensible sources. Finally, we look at time-dependent…
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…
In this paper, we study massless braneworld black holes as gravitational lenses. We find the weak and the strong deflection limits for the deflection angle, from which we calculate the positions and magnifications of the images. We compare the results obtained here with those corresponding to Schwarzschild and Reissner-Nordstrom spacetimes, and also with those found in previous works for some other braneworld black holes.
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…
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.
The Penrose process of an extremal braneworld black hole is studied. We analyze the Penrose process by two massive spinning particles collide near the horizon. By calculating the maximum energy extraction efficiency of this process, it turns out that the maximal efficiency increases as the tilde charge parameter $d$ of the braneworld blackhole decreases. Interestingly, for the negative value of $d$, the efficiency can be even larger than the Kerr case.
We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoff's theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the…
No realistic black holes localized on a 3-brane in the Randall-Sundrum infinite braneworld have been found so far. The problem of finding a static black hole solution is reduced to a boundary value problem. We solve it by means of a numerical method, and show numerical examples of a localized black hole whose horizon radius is small compared to the bulk curvature scale. The sequence of small localized black holes exhibits a smooth transition from a five-dimensional Schwarzschild black hole, which is a solution in the limit of small horizon radius. The localized black hole tends to flatten as i…
In this thesis we present the first numerical study of gravitational collapse in braneworlds within the framework of the single brane model proposed by Randall and Sundrum (RSII). We directly show that the evolutions of sufficiently strong initial data configurations result in black holes (BHs) with finite extension into the bulk. The extension changes from sphere to pancake (or cigar, seen from a different perspective) as the size of BH increases. We find preliminary evidences that BHs of the same size generated from distinct initial data profiles are geometrically indistinguishable. As such,…
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）
For an extension of the previous work on gravitational lensing by massless braneworld black holes, we investigate their microlensing phenomena and shadows and discuss how to distinguish them from standard Schwarzschild black holes and Ellis wormholes. Microlensing is known as the phenomenon in which luminosity amplification appears when a bright object passes behind a black hole or another massive object. We find that, for the braneworld black hole as well as for the Ellis wormhole, there appears luminosity reduction just before and after the amplification. This means that observation of such …
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…
In braneworld gravity models with a finite AdS curvature in the extra dimension, the AdS/CFT correspondence leads to a prediction for the lifetime of astrophysical black holes that is significantly smaller than the Hubble time, for asymptotic curvatures that are consistent with current experiments. Using the recent measurements of the position, three-dimensional spatial velocity, and mass of the black hole XTE J1118+480, I calculate a lower limit on its kinematic age of 11 Myr (95% confidence). This translates into an upper limit for the asymptotic AdS curvature in the extra dimensions of 0.08…
We study the light deflection effect and the relativistic periastron and frame-dragging precessions for a rotating black hole localized on the brane in the Randall-Sundrum braneworld scenario. Focusing on a light ray, which passes through the field of the black hole in its equatorial plane, we first calculate the deflection angle in the weak field limit. We obtain an analytical formula, involving the related perturbative parameters of the field up to the second order. We then proceed with the numerical calculation of the deflection angle in the strong field limit, when the light ray passes at …
