This is a review of current theory of black-hole dynamics, concentrating on the framework in terms of trapping horizons. Summaries are given of the history, the classical theory of black holes, the defining ideas of dynamical black holes, the basic laws, conservation laws for energy and angular momentum, other physical quantities and the limit of local equilibrium. Some new material concerns how processes such as black-hole evaporation and coalescence might be described by a single trapping horizon which manifests temporally as separate horizons.
Lecture given at ``Raychaudhuri session," ICGC-95 conference, Pune (India), December 1995. Contents: I. Introduction II. (2+1)-Dimensional Initial Values in Stereographic Projection A. The single, non-rotating black hole B. Non-rotating multi-black-holes C. ``Black Hole" Universe Initial Values III. Time Development: Enter the Raychaudhuri Equation IV. Time Development in Stereographic Projection A. The BTZ black hole spacetime B. Multi-Black-Hole Spacetimes V. Black Holes with Angular Momentum VI. Analogous 3+1-Dimensional Black Holes VII. Conclusions
The model is constructed, some features of which comes from quantum thin dust shells and is, in fact, an extension of the "no hair" property of classical black hole on a quantum level. It appears that the proposed classical analog of quantum black hole is heated, the temperature being exactly the Hawking's temperature.
We consider black hole in Einstein-Gauss-Bonnet(EGB) gravity in a dynamical setup and also the stationary black hole in recently discovered\cite{Glavan} $4$-dimensional novel Einstein-Gauss-Bonnet gravity. For dynamical EGB black hole in completely local settings we calculate the temperature associated with the horizon. For the stationary black hole in $4$-dimensional novel EGB theory we explore the thermodynamic properties including calculation of temperature and entropy.
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 shadow of a black hole can be one of the strong observational evidences for stationary black holes. If we see shadows at the center of galaxies, we would say whether the observed compact objects are black holes. In this paper, we consider a formula for the contour of a shadow in an asymptotically-flat, stationary, and axisymmetric black hole spacetime. We show that the formula is useful for obtaining the contour of the shadow of several black holes such as the Kerr-Newman black hole and rotating regular black holes. Using the formula, we can obtain new examples of the contour of the shadow…
We study thermodynamic quantities and examine the stability of a black hole in a cavity inspired by the noncommutative geometry. It turns out that thermodynamic behavior of the noncommutative black hole is analogous to that of the Reissner-Nordström black hole in the near extremal limit. Moreover, we identify the noncommutative parameter with the squared electric charge with some constants.
Singularities are common features of general relativity black holes. However, within general relativity, one can construct black holes that present no singularities. These regular black hole solutions can be achieved by, for instance, relaxing one of the energy conditions on the stress energy tensor sourcing the black hole. Some regular black hole solutions were found in the context of non-linear electrodynamics, the Bardeen black hole being the first one proposed. In this paper, we consider a planar massless scalar wave scattered by a Bardeen black hole. We compare the scattering cross sectio…
In this work, motivated by the fact that higher-dimensional theories predict the existence of black holes which differ from their four-dimensional counterpart, we analyse the geodesics and black hole shadow cast by a general non-extremal five-dimensional black hole. The system under consideration corresponds to the Chong-Cvetič-Lü-Pope (Phys. Rev.Lett.{\bf 95}, 161301 (2005)), which has the Myers--Perry black hole as a limit.
In this paper, we study the BSW process of the slowly evaporating charged black hole. It can be found that the BSW process will also arise near black hole horizon when the evaporation of charged black hole is very slow. But now the background black hole does not have to be an extremal black hole, and it will be approximately an extremal black hole unless it is nearly a huge stationary black hole.
We compute logarithmic corrections to entropy for black holes with hyperbolic horizon. For this purpose, we introduce the topological black hole and MTZ black holes in four dimensions, while in five dimensions, the topological black holes and Gauss-Bonnet black hole with negative coupling are considered. As they stand, logarithmic corrections are problematic because small black holes with positive heat capacity have negative energies. However, introducing the background state of extremal black hole, the logarithmic corrections are performed for black hole with hyperbolic horizon.
We study thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization, and does not favor the Bousso-Hawking normalization.
By using an analytic solution of the Teukolsky equation in the Kerr-de Sitter and Kerr-Newman-de Sitter geometries, an analytic expression of the absorption rate formulae for these black holes is calculated.
The classical first law of thermodynamic for Kerr-Newmann black hole (KNBH) is generalized to that in quantum form on event horizon. Then four quantum conservation laws on the KNBH equilibrium radiation process are derived, and Bekenstein-Hawking's relation S=A/4 is recovered. It can be argued that the classical entropy of black hole arise from the quantum entropy of field quanta or quasi-particles inside the hole.
By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and weak cosmic censorship conjecture (WCCC) with two types of boundary conditions, i.e., the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in the asymptotically at space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and nearextremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change …
This paper describes that the superconducting cosmic strings can be connected to an electrically charged black hole, and can be considerd as the hair of black hole. What the no-hair theorems show is that a large amount of information is lost when a body collapses to form a black hole. In addition, the no-hair theorem has not been proved for the Yang-Mills field. This paper proves and claims that the superconducting cosmic strings can be connected to an electrically charged hole when the current inside these strings and black holes approaches the critical value. Because, this state is the final…
The superradiant stability of higher dimensional non-extremal Reissner-Nordstrom black hole under charged massive scalar perturbation is analytically studied. We extend our previous studies of four- and five-dimensional non-extremal Reissner-Nordstrom black hole cases to six-dimensional case. By analyzing the derivative of the effective potential with an analytical method, we find that no potential well exists outside the outer horizon of the black hole for the superradiant scalar modes. This means that there is no black hole bomb for the system consisting of six-dimensional Reissner-Nordstrom…
In Randall-Sundrum single-brane (RS-II) model, it was conjectured that there is no static large black hole localized on the brane based on adS/CFT correspondence. Here we consider the phase diagram of black objects in the models extended from the RS-II model. We propose a scenario for the phase diagram consistent with the classical black hole evaporation conjecture. The proposed scenario indicates the existence of a rich variety of the families of black objects.
We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.
We study thermodynamic quantities of an acoustic black hole and its thermodynamic stability in a cavity based on the generalized uncertainty principle. It can be shown that there is a minimal black hole which can be a stable remnant after black hole evaporation. Moreover, the behavior of the free energy shows that the large black hole is stable too. Therefore, the acoustic black hole can decay into the remnant or the large black hole.
We introduce three approaches to generate curvature invariants that transform covariantly under a conformal transformation of a four dimensional spacetime. For any black hole conformally related to a stationary black hole, we show how a set of conformally covariant invariants can be combined to produce a conformally covariant invariant that detects the event horizon of the conformally related black hole. As an application we consider the rotating dynamical black holes conformally related to the Kerr-NUT-(Anti)-de Sitter spacetimes and construct an invariant that detects the conformal Killing h…
The Event Horizon Telescope, a global submillimeter wavelength very long baseline interferometry array, produced the first image of supermassive black hole M87* showing a ring of diameter $θ_d= 42\pm 3\,μ$as, inferred a black hole mass of $M=(6.5 \pm 0.7) \times 10^9 M_\odot $ and allowed us to investigate the nature of strong-field gravity. The observed image is consistent with the shadow of a Kerr black hole, which according to the Kerr hypothesis describes the background spacetimes of all astrophysical black holes. The hypothesis, a strong-field prediction of general relativity, may be viol…
In this work, starting from a spherically symmetric scale--dependent black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we get and discuss the shape of its shadow.
We investigate $4D$ Einstein-Gauss-bonnet gravity coupled to exponential electrodynamics in AdS background and found a static, spherically symmetric exact black hole solution. The horizon structure of black hole is discussed. Treating the cosmological constant as pressure, we drive first law of black hole thermodynamics in extended phase space. We compute the electrostatic potential and vacuum polarization of the black hole. To study local thermodynamical stability specific heat of the black hole is computed. Finally, we study Helmholtz free energy to analyse the global stability of black hole…
As an example of a black hole in a non-flat background a composite static spacetime is constructed. It comprises a vacuum Schwarzschild spacetime for the interior of the black hole across whose horizon it is matched on to the spacetime of Vaidya representing a black hole in the background of the Einstein universe. The scale length of the exterior sets a maximum to the black hole mass. To obtain a non-singular exterior, the Vaidya metric is matched to an Einstein universe. The behaviour of scalar waves is studied in this composite model.
In this paper we study the thermodynamics and state space geometry of regular black hole solutions such as Bardeen black hole, Ayón-Beato and García black hole, Hayward black hole and Berej-Matyjasek-Trynieki-Wornowicz black hole. We find that all these black holes show second order thermodynamic phase transitions(SOTPT) by observing discontinuities in heat capacity-entropy graphs as well as the cusp type double point in free energy-temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curva…
The superradiant stability of asymptotically flat D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is analytically studied. Recently, an analytical method has been proposed by the author and used to prove that five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable under charged massive scalar perturbation. We apply this analytical method in the D-dimensional extremal Reissner-Nordstrom black hole cases and prove that the D-dimensional Reissner-Nordstrom black holes are all superradiantly stable under charged mas…
In this short paper we discuss the possibility of testing the nature of astrophysical black holes using the recently observed black hole mergers. We investigate the possibility that a secondary black hole is created in the merger of two astrophysical black holes and discuss potential astrophysical signatures. We point out that black hole mergers are a possible astrophysical mechanism for the creation of quantum black holes with masses close to the Planck mass.
We obtain a charged, rotating and accelerating black hole solution in the $f(R)$ gravity and calculate thermodynamic quantities of the black hole in the slow acceleration regime. We then find that the black hole can be super-entropic in a certain condition. After investigating the null hypersurface of the black hole, we show that there exist super-entropic black holes whose null hypersurface caustics only form inside the Cauchy horizon.
In this paper we derive a class of rotating embedded black holes. Then we study Hawking's radiation effects on these embedded black holes. The surface gravity, entropy and angular velocity are given for each of these black holes.
We derive a class of non-stationary embedded rotating black holes and study the Hawking's radiation effects on these embedded black holes. The surface gravity, entropy and angular velocity, which are three important properties of black holes, are presented for each of these embedded black holes.
The rates at which the mass and angular momentum of a small black hole change as a result of a tidal interaction with a much larger black hole are calculated to leading order in the small mass ratio. The small black hole is either rotating or nonrotating, and it moves on a circular orbit in the equatorial plane of the large Kerr black hole. The orbits are fully relativistic, and the rates are computed to all orders in the orbital velocity V < V_{isco}, which is limited only by the size of the innermost stable circular orbit. We show that as V \to V_{isco}, the rates take on a limiting value th…
Null Geodesics, Thermodynamics, Weak Gravitational Lensing, and Black Hole Shadow Characteristics of a Frolov Regular Black Hole with Constraints from EHT Observations
We calculate the black hole mass distribution function that follows from the random emission of quanta by Hawking radiation and with this function we calculate the black hole mass fluctuation. From a complete different perspective we regard the black hole as quantum mechanical system with a quantized event horizon area and transition probabilities among the various energy levels and then calculate the mass dispersion. It turns out that there is a perfect agreement between the statistical and the microscopic calculations if and only if the area spectrum is linear. Accordingly, the quantum mecha…
To provide an analytic verification of the nature of phase transition at the critical point of $P-V$ criticality, the original expressions of Ehrenfest equations have been introduced directly. By treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume respectively, we carry out analytical check of classical Ehrenfest equations. To show that our approach is universal, we investigate not only higher-dimensional charged AdS black holes, but also rotating AdS black holes. Not only are the examples of Einstein gravity shown, but also the example of modifie…
The simplest solution to the black hole information loss problem is to eliminate black holes. Modifications of Einstein gravity which accomplish this are discussed and the possibility that string theory is free of black holes is considered.
Geodesic completeness needs existence near the horizon of the black hole of "white hole" geodesics coming from the region inside of the horizon. Here we give the classification of all such geodesics with the energies $E/m \le 1$ for the Schwarzschild and Kerr's black hole. The collisions of particles moving along the "white hole" geodesics with those moving along "black hole" geodesics are considered. Formulas for the increase of the energy of collision in the centre of mass frame are obtained and the possibility of observation of high energy particles arriving from the black hole to the Earth…
We study about an approximation method of the Hawking radiation. We analyze an massless scalar field in exotic black hole backgrounds models which have peculiar properties in black hole thermodynamics (monopole black hole in SO(3) Einstein-Yang-Mills-Higgs system and dilatoic black hole in Einstein-Maxwell-dilaton system). A scalar field is assumed not to be couple to matter fields consisting of a black hole background. Except for extreme black holes, we can well approximate the Hawking radiaition by `black body' one with Hawking temperature estimated at a radius of a critical impact parameter…
Lecture notes for a 'Part III' course 'Black Holes' given in DAMTP, Cambridge. The course covers some of the developments in Black Hole physics of the 1960s and 1970s.
The objectivity of black hole entropy is discussed in the particular case of a Schwarzchild black hole. Using Jaynes' maximum entropy formalism and Euclidean path integral evaluation of partition function, it is argued that in the semiclassical limit when the fluctutation of metric is neglected, the black hole entropy of a Schwarzchild black hole is equal to the maximal information entropy of an observer whose sole knowledge of the black hole is its mass. Black hole entropy becomes a measure of number of its internal mass eigenstates in accordance with the Boltzmann principle only in the limit…
Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.
In this work, starting from a spherically symmetric polytropic black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we obtain and discuss the shape of its shadow. Some other physical features as the Hawking temperature and emission rate of the rotating polytropic black hole solution are also discussed.
Mean first passage time and the Kramers escape rate of phase transitions for the Bardeen-AdS-class black hole
Northwest University（西北大学）；Institute of Modern Physics, Northwest University（西北大学现代物理研究所）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）；Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西理论物理前沿重点实验室）；Fundamental Discipline Research Center for Quantum Science and technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）
In this paper, we investigate the Weak Cosmic Censorship Conjecture in nearly extremal Kerr black hole by absorbing particles . In previous work, they ignore the process of black hole absorbing particles. They assume the whole particle can be absorbed and the overspinning occurs. However, it is questionable whether the whole particle can be absorbed. Therefore, we will investigate it in this paper. We consider the absorption process of a particle with finite size. During this absorption process, the black hole's parameters will change. This change will prevent the rest part of particle enter b…
We study the thermodynamic properties of the black hole derived in Hořava-Lifshitz (HL) gravity without the detailed-balance condition. The parameter $Ξ=ε^2$ in the HL black hole plays the same role as that of the electric charge in the RN-AdS black hole. By analogy, we treat the parameter $Ξ$ as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy the two black holes have very different thermodynamic properties. By calculating …
Charged black hole solutions with pion hair are discussed. These can be used to study monopole black hole catalysis of proton decay. There also exist multi- black hole skyrmion solutions with BPS monopole behavior.
In this paper, for dimensionally continued gravity coupled to Born-Infeld electromagnetic field, we construct topological black holes in diverse dimensions and construct dyonic black holes in general even dimensions. We study thermodynamics of the black holes and obtain first laws. We study thermal phase transitions of the black holes in $T$-$S$ plane and find van der Waals-like phase transitions for even-dimensional spherical black holes, such phase transitions are not found for other types of black holes constructed in this paper.
We discuss an evaporation of (2+1)-dimensional black hole by using quantum gravity holding in the vicinity of the black hole horizon. It is shown that the black hole evaporates at a definite rate by emitting matters through the quantum tunneling effect. A relation of the present formalism to the black hole entropy is briefly commented.
We extend some solutions for black holes in the Randall-Sundrum theory with a single brane. We consider a generalised version of the extremal black hole on the brane in n + 1 dimensions and determine an asymptotic value of the geometry for large black holes.
We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sfetsos black hole and a regular black hole with Dagum Distribution Function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The accreting fluid is being classified through equation of state according to features of regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. It is noted that three velocity depends on critical points and equation of state parameter on phase space.
We describe the gravitational degrees of freedom of the Schwarzschild black hole by one free variable. We introduce an equation which we suggest to be the Schroedinger equation of the Schwarzschild black hole corresponding to this model. We solve the Schroedinger equation explicitly and obtain the mass spectrum of the black hole as such as it can be observed by an observer very far away and at rest relative to the black hole. Our equation implies that there is no singularity inside the Schwarzschild black hole, and that the black hole has a certain ground state in which its mass is non-zero.
We show it is possible for the information paradox in black hole evaporation to be resolved classically. Using standard junction conditions, we attach the general closed spherically symmetric dust metric to a spacetime satisfying all standard energy conditions but with a single point future c-boundary. The resulting Omega Point spacetime, which has NO event horizons, nevertheless has black hole type trapped surfaces and hence black holes. But since there are no event horizons, information eventually escapes from the black holes. We show that a scalar quintessence field with an appropriate expo…
We study phase transitions between black holes with scalar hair and topological black holes in asymptotically anti-de Sitter spacetimes. As the ground state solutions, we introduce the non-rotating BTZ black hole in three dimensions and topological black hole with hyperbolic horizon in four dimensions. For the temperature matching only, we show that the phase transition between black hole with scalar hair (Martinez-Troncoso-Zanelli black hole) and topological black hole is second-order by using differences between two free energies. However, we do not identify what order of the phase transitio…
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
