The Schwarzschild star is an ultracompact object beyond the Buchdahl limit, which has Schwarzschild geometry outside its surface and positive pressure in the external layer which vanishes at the surface. Recently it has been shown that the Schwarzschild star is stable against spherically symmetric perturbations. Here we study arbitrary axial nonspherical perturbations, and show that the observable quasinormal modes can be as close to the Schwarzschild limit as one wishes, what makes the Schwarzschild star a very good mimicker of a black hole. The decaying time-domain profiles prove that the Schwarzschild star is stable against nonspherical perturbations as well. Another peculiar feature is the absence of echoes at the end of the ringdown. Instead we observe a nonoscillating mode which might belong to the class of algebraically special modes. At asymptotically late times, Schwarzschildian power-law tails dominate in the signal.
In the context of ghost-free, infinite derivative gravity, we will provide a quantum mechanical framework in which we can describe astrophysical objects devoid of curvature singularity and event horizon. In order to avoid ghosts and singularity, the gravitational interaction has to be nonlocal, therefore, we call these objects as nonlocal stars. Quantum mechanically a nonlocal star is a self-gravitational bound system of many gravitons interacting nonlocally. Outside the nonlocal star the spacetime is well described by the Schwarzschild metric, while inside we have a non-vacuum spacetime metri…
Can the observation of the "shadow" allow us to distinguish a black hole from a more exotic compact object? We study the motion of photons in a class of vacuum static axially-symmetric space-times that is continuously linked to the Schwarzschild metric through the value of one parameter that can be interpreted as a measure of the deformation of the source. We investigate the lensing effect and shadow produced by the source with the aim of comparing the expected image with the shadow of a Schwarzschild black hole. In the context of astrophysical black holes we found that it may not be possible …
Black holes and wormholes are solutions of Einstein's field equations, both of which, from afar, look like a central mass. We show here that although at large distances both behave like Newtonian objects, close to the event horizon or to the throat, black holes and wormholes have different tidal effects on stars, due to their respective geometries. We quantify this difference by a numerical procedure in the Schwarzschild black hole and the exponential wormhole backgrounds, and compare the peak fallback rates of tidal debris in these geometries. The tidal disruption rates in these backgrounds a…
Long-term stable nonlinear evolutions of ultracompact black-hole mimickers
University of Cambridge（剑桥大学）；KU Leuven（荷语鲁汶大学）；Perimeter Institute for Theoretical Physics（理论物理珀米特研究所）；Johns Hopkins University（约翰斯·霍普金斯大学）；Caltech（加州理工学院）
The frozen star is a non-singular, ultracompact object that, to an external observer, looks exactly like a Schwarzschild black hole, but with a different interior geometry and matter composition. The frozen star needs to be sourced by an extremely anisotropic fluid, for which the sum of the radial pressure and energy density is either vanishing or perturbatively small. Here, we show that this matter can be identified with the string fluid resulting from the decay of an unstable $D$-brane or a brane-antibrane system at the end of open-string tachyon condensation. The string fluid corresponds to…
We undertake the task of studying the non-linear dynamics of quantum gravity motivated alternatives to black holes that in the classical limit appear as ultra-compact shells of matter. We develop a formalism that should be amenable to numerical solution in generic situations. For a concrete model we focus on the spherically symmetric AdS black bubble -- a shell of matter at the Buchdahl radius separating a Schwarzschild exterior from an AdS interior. We construct a numerical code to study the radial dynamics of and accretion onto AdS black bubbles, with exterior matter provided by scalar field…
The central theme of this thesis is the study and analysis of black hole mimickers. The concept of a black hole mimicker is introduced, and various mimicker spacetime models are examined within the framework of classical general relativity. The mimickers examined fall into the classes of regular black holes and traversable wormholes under spherical symmetry. The regular black holes examined can be further categorised as static spacetimes, however the traversable wormhole is allowed to have a dynamic (non-static) throat. Astrophysical observables are calculated for a recently proposed regular b…
Ultracompact objects with photonspheres are known to mimic many observational features of black holes. It has been suggested that anomalous tidal heating or the presence of resonances in gravitational wave signals would be a clear imprint of a surface or absence of a horizon. Such claims and studies are all based on a frequency-domain analysis, assuming stationarity. Here we show that the object needs to first "fuel-up" until it reaches the stationary regime. The presence of a stable light ring and large light-travel times inside the object may in fact delay enormously the "charging-up" and ef…
We discuss the astrophysical and cosmological implications of having primordial thermal 2-2-hole remnants as dark matter. Thermal 2-2-holes emanate in quadratic gravity as horizonless classical solutions for ultracompact distributions of relativistic thermal gas. In contrast to a large 2-2-hole that imitates the thermodynamic behaviour of a black hole, a small 2-2-hole at late stages of evaporation behaves as a stable remnant with the mass approaching a minimal value. These remnants as all dark matter can satisfy the corresponding observational constraints provided that both the formation and …
It is shown that the extremal Reissner-Nordström black hole, the non-extremal one with multiple scattering particles, and the Schwarzschild black hole with radial head-on particles are stable under the collision of the particles near the horizon, if the back-reaction effect and the effect generated by gravity of particles are involved. Moreover, the collision near Reissner-Nordström black holes with astrophysically typical mass can not generate the Planck-scale center-of-mass energy. However, the head-on collision near the typical primordial black hole could just occur at the Planck-energy sca…
The inclusion of the Weyl squared term in the gravitational action is one of the most simple, yet non trivial modifications to General Relativity at high energies. Nevertheless the study of the spherically-symmetric vacuum solutions of this theory has received much attention only in recent times. A new type of asymptotically flat wormhole which does not match symmetrically at a finite radius with another sheet of the spacetime is presented. The outer spacetime is characterized by a newtonian potential with a Yukawa correction, and has gravitational properties that can be arbitrarily close to t…
A Regge--Wheeler analysis is performed for a novel black hole mimicker `the regular black hole with asymptotically Minkowski core', followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order WKB approximation is computed for spin zero and spin one perturbations of the candidate spacetime. Subsequently, numerical results analysing the respective fundamental modes are compiled for various values of the $a$ parameter (which quantifies the distortion from Schwarzschild spacetime), and for various multipole numbers $\ell$. Both electromagnetic spin one…
The microscopic structure of black holes remains a challenging subject. In this paper, based on the well-accepted fact that black holes can be mapped to thermodynamic systems, we make a preliminary exploration of the microscopic structure of the thermodynamically stable Schwarzschild anti-de-Sitter (SAdS) black hole. In accordance with the number density and thermodynamic scalar curvature, we give the interaction potential among the molecules of thermodynamically stable SAdS black holes and analyze its effectiveness. Moreover, we derive the thermo-correction to the equation of state for such b…
Generally, the Schwarzschild black hole was proved stable through two different methods: the mode-decomposition method and the integral method. In the paper, we show the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of the tortoise coordinates in the perturbation equations. Subsequently, the perturbation equation in the Schwarzschild coordinates is shown not sufficient for the stable study.
The stability of the Schwarzschild black hole is studied. Using the Painlevé coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) of the Schwarzschild black hole. We study the stable problems of the black-hole-connected region. The conclusions are: (1) in the black-hole-connected region, the initially regular perturbation fields must have real frequency or complex frequency whose imaginary must not be greater than -1/4m, so the black-hole-connected regionis stable in physicist…
The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ has (areal) radius $r_{\rm isco}= 6M G/c^2$. If the particle is endowed with mass $μ(\ll M)$, it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts $Δr_{\rm isco}$ and $ΔΩ_{\rm isco}$ in the ISCO's radius and frequency, at leading order in the mass ratio $μ/M$. We obtain, in the Lorenz gauge, $Δr_{\rm isco}=-3.269 (\pm 0.003)μG/c^2$ and $ΔΩ_{\rm isco}/Ω_{\rm isco}=0.4870 (\pm 0.0006) μ/M$. We discuss the…
Carefully analyze influence of the tortoise coordinates r* and t on the stable study of the Schwarzschild black hole. Actually, one should be cautious in using the compact property of the perturbation field: it is true only with respect with the coordinate r and proper time or "good time", not the tortoise coordinates r* and t. Therefore, the mathematical proof used in reference [7] is incorrect because of it relying on the compact property of the perturbation fields. The Schwarzschild black hole might be unstable[1]-[5]
A Damour-Solodukhin wormhole with a metric which is similar to a Schwarzschild black hole seems to be a black hole mimicker since it is difficult to distinguish them by practical astrophysical observations. In this paper, we investigate a center-of-mass energy for the collision of two test particles in the Damour-Solodukhin wormhole spacetime. We show that the center-of-mass energy for the head-on collision of the particles is large if the difference between the metrics of the wormhole and the black hole is small. To deeply understand the high energy particle collision, we generalize the head-…
We study the gravitational radiation emitted by a massive point particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. We consider both even- and odd-parity perturbations and describe them using the two gauge-invariant master functions of Cunningham, Price, and Moncrief. We obtain, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over of a large number of modes, and their unregularized counterparts co…
The stability of the Schwarzschild black hole is studied. Regge and Wheeler treated the problem first at 1957 and obtained the dynamical equations for the small perturbation. There are two kinds of perturbations: odd one and even one. Using the Painlevé coordinate, we reconsider the odd perturbation and find that: the white-hole-connected universe(r>2m, see text) is unstable. Because the odd perturbation may be regarded as the angular perturbation, therefore, the physical mean to it may be that the white-hole-connected universe is unstable with respect to the rotating perturbation.
In a recent paper we investigated stationary, relativistic Bondi-type accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their stability, using the method developed by Moncrief. The analysis applies to perturbations satisfying the potential flow condition. We prove that global isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable, assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de Sitter geometries and polytropic flows in Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary condit…
In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase tra…
Marginally stable circular orbits (MSCOs) of a massive test particle are investigated in the spacetime geometry of Schwarzschild black hole surrounded by quintessence. For that matter we consider three important scenarios where the equation of state parameter $ω_{q}$, has one of the following forms (i) $ω_q=-1$ (ii) $ω_q=-2/3$ and (iii) $ω_q= -1/3$. The existence of such marginally stable circular orbits in these scenarios depend on the range of normalization factor $α$. Briefly, we show that in the first case such orbits exist only if $0<α<4/16875$. Moreover in the second case which is a spec…
We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locall…
We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their s…
Usually alternative theories of gravity imply deviations from the well-known Kerr space-time, a model of an isolated black hole in General Relativity. In the dominant order, the deformed Kerr metric, free of closed time-like curves outside the event horizon, has been suggested recently by Johannsen and Psaltis. It has a single deformation parameter which is not constrained by the current observations, allowing, thereby, for a kind of unified and simple phenomenological description of black holes in various theories of gravity. Here we consider a number of classical and quantum phenomena of rad…
We study the circular orbits of charged particles around a weakly charged Schwarzschild black hole immersed in a weak, axisymmetric magnetic field. We start by reviewing the circular orbits of neutral particles and charged particles around only weakly charged and only weakly magnetized black holes. The case of a weakly magnetized and charged black hole is investigated then. In particular, we study the effect of the electromagnetic forces on the charged particles innermost stable circular orbits. We show that negative energy stable circular orbits are possible and that two bands of charged part…
We use the Kruskal time coordinate T to define the initial time. By this way, it naturally divides the stable study into one connected with the two regions: the white-hole-connected region and the black-hole-connected region. The union of the two regions covers the Schwarzschild space-time (r>2m). We also obtain the very reasonable conclusion: the white-hole-connected region is instable; whereas the black-hole-connected region is stable. If we take the instability with caution and seriousness, it might be not unreasonable to regard that the Schwarzschild black hole might be instable too.
Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits ar…
We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(dθ^2 +\sin ^2 θdϕ^2)$ with $f(r) = 1 -\frac{2Gm}{r} + 2 b r -\fracΛ{3}r^2$. This is an alternative to the well known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In the SRAdS spacetime the repulsion that leads to stability of the shell comes from a negative Rindler te…
Can a dynamically robust bosonic star (BS) produce an (effective) shadow that mimics that of a black hole (BH)? The BH shadow is linked to the existence of light rings (LRs). For free bosonic fields, yielding mini-BSs, it is known that these stars can become ultra-compact - i.e., possess LRs - but only for perturbatively unstable solutions. We show this remains the case even when different self-interactions are considered. However, an effective shadow can arise in a different way: if BSs reproduce the existence of an innermost stable circular orbit (ISCO) for timelike geodesics (located at $r_…
We discuss quantum black holes in asymptotically safe quantum gravity with a scale identification based on the Kretschmann scalar. After comparing this scenario with other scale identifications, we investigate in detail the Kerr-(A)dS and Schwarzschild-(A)dS space-times. The global structure of these geometries is studied as well as the central curvature singularity and test particle trajectories. The existence of a Planck-sized, extremal, zero temperature black hole remnant guarantees a stable endpoint of the evaporation process via Hawking radiation.
We discuss the properties of the previously constructed model of a Schwarzschild black hole interior where the singularity is replaced by a regular bounce, ultimately leading to a white hole. The model is semiclassical in nature and uses as a source of gravity the effective stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, and a minimum spherical radius is a few orders of magnitude larger than the Planck length, so that the effects of quantum gravity should be still negligible. We estimate the other quantum contributions to the effective SET, caused by a nontri…
In higher-dimensional Schwarzschild black hole spacetimes, there are no stable bound orbits of particles. In contrast to this, it is shown that there are stable bound orbits in a five-dimensional black lens spacetime.
We compute the quasinormal spectra for scalar, Dirac and electromagnetic perturbations of the Schwarzschild-de Sitter geometry in the framework of scale-dependent gravity, which is one of the current approaches to quantum gravity. Adopting the widely used WKB semi-classical approximation, we investigate the impact on the spectrum of the angular degree, the overtone number as well as the scale-dependent parameter for fixed black hole mass and cosmological constant. We summarize our numerical results in tables, and for better visualization, we show them graphically as well. All modes are found t…
We have proposed a model geometry for the interior of a regular black hole mimicker, the frozen star, whose most startling feature is that each spherical shell in its interior is a surface of infinite redshift. The geometry is a solution of the Einstein equations which is sourced by an exotic matter with maximally negative radial pressure. The frozen star geometry was previously presented in singular coordinates for which $-g_{tt}$ and $g^{rr}$ vanish in the bulk and connect smoothly to the Schwarzschild exterior. Additionally, the geometry was mildly singular in the center of the star. Here, …
The stable geodesics in Schwarzschild geometry can not approach the center closer than the radius of the photon sphere, 3/2 times the Schwarzschild radius. In other words, massive particles moving along geodesics that cross the photon sphere do not escape, they fall into the black hole.
Recently, a novel model for a regular black hole was advocated which possesses an asymptotically Minkowski core implemented via an exponential suppression (in the core region) of the Misner-Sharp quasi-local mass. Using this regular black hole as a template, we shall construct a spherically symmetric thin-shell traversable wormhole using the "cut-and-paste" technique, thereby constructing yet another black hole mimicker. The surface stress-energy at the wormhole throat is calculated, and the stability of the wormhole is analyzed. An important result is that, (as compared to their Schwarzschild…
Time-dependent spherically-symmetric perturbations of Schwarzschild black holes are studied within torsion bigravity, i.e., within generalized Einstein-Cartan theories where the dynamical torsion carries massive spin-2 excitation. We reduce linearized perturbations to a Zerilli-like equation. The structure of the potential entering the latter Zerilli-like equation has two important consequences. First, in order to avoid the presence of singularities in generic perturbations, one must restrict the range (or inverse mass) of the spin-2 excitation to be (essentially) smaller than the radius of th…
We study thermodynamic quantities and phase transitions of a spherically symmetric Schwarzschild black hole by taking into account the back reaction through the conformal anomaly of matter fields, and show that there exists an additional phase transition to the conventional Hawking-Page phase transition. The small black hole is more probable than the hot flat space above a second critical temperature, while it is less probable than the hot flat space in the classical Schwarzschild black hole. However, the unstable small black hole eventually should decay into the stable large black hole becaus…
