On the Existence of Conformally Coupled Scalar Field Hair for Black Holes in (Anti-)de Sitter Space

The Einstein-conformally coupled scalar field system is studied in the presence of a cosmological constant. We consider a massless or massive scalar field with no additional self-interaction, and spherically symmetric black hole geometries. When the cosmological constant is positive, no scalar hair can exist and the only solution is the Schwarzschild–de Sitter black hole. When the cosmological constant is negative, stable scalar field hair exists provided the mass of the scalar field is not too large.     

Entropy Evolution in the Interior Volume of a Charged $f(R)$ Black Hole *

Based on the 4-dimensional black hole solution of $f(R)$ theory coupled to a nonlinear Maxwell field, we calculate the interior volume of a charged $f(R)$ black hole using the method proposed by Christodoulou and Rovelli. Considering massless scalar field in the interior volume and Hawking radiation carrying only energy, we calculate the entropy of the scalar field inside a charged $f(R)$ black hole and investigate the evolution of the entropy under Hawking radiation. In the meantime, the evolution of the Bekenstein-Hawking entropy under Hawking radiation has also been calculated. Based on these results, the proportional relation is obtained between the evolution of the scalar field entropy and the evolution of Bekenstein-Hawking entropy under Hawking radiation. According to the result, we investigate and discuss how the modified coefficient $b$ in $f(R)$ gravity theory affects the evolution relation between the two types of entropy. It is shown that the radiation rate for Hawking radiation of a charged $f(R)$ black hole can increase with the modified coefficient $b$.     

Thermodynamics of warped anti-de Sitter black holes under scattering of scalar field

We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field.Under scattering,conserved quantities can be transferred from the scalar field to the black hole,thereby changing the state of the black hole.We determine that the changes in the black hole are well coincident with the laws of thermodynamics.In particular,the Hawking temperat-ure of the black hole cannot be zero in the process as per the third law of thermodynamics.Furthermore,the black hole cannot be overspun bevond the extremal condition under the scattering of any mode of the scalar field.     

Entropy of quantum field in toroidal black hole without brick wall

In this paper the entropy of a toroidal black hole due to a scalar field is investigated by using the DLM scheme. The entropy is renormalized to the standard Bekenstein-Hawking formula with a one-loop correction arising from the higher curvature terms of the gravitational action. For the scalar field, the renormalized Newton constant and two renormalized coupling constants in the toroidal black hole are the same as those in the Reissner-Nordstrom black hole except for other one.     

Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity

This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.     

Black holes in the Brans-Dicke

It is shown that a stationary space containing a black hole is a solution of the Brans-Dicke field equations if and only if it is a solution of the Einstein field equations. This implies that when the star collapses to form a black hole, it loses that fraction (about 7%) of its measured gravitational mass that arises from the scalar interaction. This mass loss is in addition to that caused by emission of scalar or tensor gravitational radiation. Another consequence is that there will not be any scalar gravitational radiation emitted when two black holes collide.     

Black holes in massive gravity: quasi-normal modes of scalar perturbations

We have studied quasinormal modes of scalar perturbations of a black hole in massive gravity. The parameters of the theory, such as the mass of the black hole, the scalar charge of the black hole and the spherical harmonic index is varied to see how the corresponding quasinormal frequencies change. We have also studied the massive scalar field perturbations. Most of the work is done using WKB approach while sections are devoted to compute quasinormal modes via the unstable null geodesics approach and the Pöschl–Teller approximation. Comparisons are done with the Schwarzschild black hole.     

Black-hole singularities: a new critical phenomenon

The singularity inside a spherical charged black hole, coupled to a spherical, massless scalar field is studied numerically. The profile of the characteristic scalar field was taken to be a power of advanced time with an exponent alpha>0. A critical exponent alpha(crit) exists. For exponents below the critical one (alphaalpha(crit)) an all-encompassing, spacelike singularity evolves, which completely blocks the "tunnel" inside the black hole, preventing the use of the black hole as a portal for hyperspace travel.     

Dilaton driven Hawking radiation in AdS2 black hole

A recent study shows that Hawking radiation of a massless scalar field does not appear on the two-dimensional AdS₂ black hole background. We shall study this issue by calculating absorption and reflection coefficients under dilaton coupling with the matter field. If the scalar field does not couple to the dilaton, then it is fully absorbed into the black hole without any outgoing mode. On the other hand, once it couples to the dilaton field, the outgoing mode of the massless scalar field exists, and the nontrivial Hawking radiation appears. Finally, we comment on this dilaton dependence of Hawking radiation in connection with a three-dimensional black hole.     

Thermodynamics of a Charged Hairy Black Holein (2+1) Dimensions

In this paper we study thermodynamics, statistics and spectroscopic aspects of a charged black hole with a scalar hair coupled to the gravity in (2+1) dimensions. We obtained effects of the black hole charge and scalar field on the thermodynamical and statistical quantities. We find that scalar charge may increase entropy, temperature and probability, while may decrease black hole mass, free and internal energy. Also electric charge increases probability and decreases temperature and internal energy. Also we investigate stability of the system and find that the thermodynamical stability exists.     

Stochastic equations in black hole backgrounds and non-equilibrium fluctuation theorems

We apply the non-equilibrium fluctuation theorems developed in the statistical physics to the thermodynamics of black hole horizons. In particular, we consider a scalar field in a black hole background. The system of the scalar field behaves stochastically due to the absorption of energy into the black hole and emission of the Hawking radiation from the black hole horizon. We derive the stochastic equations, i.e. Langevin and Fokker-Planck equations for a scalar field in a black hole background in the ?→0 limit with the Hawking temperature ?κ/2π fixed. We consider two cases, one confined in a box with a black hole at the center and the other in contact with a heat bath with temperature different from the Hawking temperature. In the first case, the system eventually becomes equilibrium with the Hawking temperature while in the second case there is an energy flow between the black hole and the heat bath. Applying the fluctuation theorems to these cases, we derive the generalized second law of black hole thermodynamics. In the present paper, we treat the black hole as a constant background geometry.Since the paper is also aimed to connect two different areas of physics, non-equilibrium physics and black holes physics, we include pedagogical reviews on the stochastic approaches to the non-equilibrium fluctuation theorems and some basics of black holes physics.     

Massive Charged Quasinormal Modes of a Reissner-Nordström Black Hole

Using the WKB method and HYBRD program, we evaluate the low-lying massive charged scalar and Dirac field quasinormal modes (QNMs) of a Reissner-Nordström black hole. We discuss the real and imaginary parts of QNMs vary with the charge of black hole, the masses and charges of scalar and Dirac fields.     

On the Møller Energy Associated with Black Holes

In this paper, we consider both Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation) analogs of the energy-momentum definition of Møller in order to explicitly evaluate the energy distribution (due to matter and fields including gravity) associated with a general black hole model which includes several well-known black holes. To calculate the special cases of energy distribution, here we consider eight different types of black hole models such as anti-de Sitter Cmetric with spherical topology, charged regular black hole, conformal scalar dyon black hole, dyadosphere of a charged black hole, regular black hole, charged topological black hole, charged massless black hole with a scalar field, and the Schwarzschild-de Sitter space-time. Our teleparallel gravitational result is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in teleparallel equivalent of general relativity but also in any teleparallel model. This paper also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is the powerful concept to calculate energy distribution in a given space-time.     

Superradiant Instability of D-Dimensional Reissner–Nordstr?m Black Hole Mirror System

We analytically study the superradiant instability of charged massless scalar field in the background of D-dimensional Reissner–Nordstr¨om(RN) black hole caused by mirror-like boundary condition. By using the asymptotic matching method to solve the Klein–Gordon equation that governs the dynamics of scalar field, we have derived the expressions of complex parts of boxed quasinormal frequencies, and shown they are positive in the regime of superradiance.This indicates the charged scalar field is unstable in D-dimensional Reissner–Nordstr¨om(RN) black hole surrounded by mirror. However, the numerical work to calculate the boxed quasinormal frequencies in this system is still required in the future.     

动态广义球对称含荷黑洞的量子熵

计算了广义球对称含荷黑洞视界上标量场的量子态数和自由能，得到了黑洞熵与视界面积成 正比的结论，表明黑洞熵就是其视界上的量子态的熵．考虑广义不确定原理对黑洞熵的影响 ，采用二维膜模型，克服了brick-wall模型中的发散困难，计算中无须任何截断，且brick- wall模型中的小质量近似也可以避免．对视界外二维膜上的量子场的熵做了级数展开讨论， 得到了一些值得探讨的结论． 关键词： 广义不确定原理 黑洞熵 视界 截断     

Quasinormal modes of the scalar field in five-dimensional Lovelock black hole spacetime

In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and oscillate more slowly in the Lovelock black hole background.     

Statistical-Mechanical Entropy of Garfinkle-Horowitz-Strominger Black Hole

Taking WKB approximation to solve the scalar field equation in the Garfinkle-Horowitz-Strominger (GHS) black hole spacetime, we can get the classical momenta. Substituting the classical momenta into state density equation corrected by the generalized uncertainty principle, we will obtain the number of quantum states with energy less than ω. It is convergent in the neighborhood of the horizon. Then, it is used to calculate the statistical-mechanical entropy of the scalar field in the GHS black hole spacetime. The calculation shows that the entropy is proportional to the horizon area.     

Quasinormal modes and absorption of a massless scalar field for the magnetic Gauss–Bonnet black hole

We study the massless scalar quasinormal frequencies of an asymptotically flat static and spherically symmetric black hole with a nonzero magnetic charge in four-dimensional extended scalar-tensor-Gauss–Bonnet theory. The results show that the real part of the quasinormal frequency becomes larger and the imaginary part becomes smaller with increasing the magnetic charge or the angular harmonic index. The existence of magnetic charges will reduce the damping of scalar perturbation, but increase the frequency. We also study the absorption cross-section of the scalar field in this black hole. We find that its curve will become lower as the magnetic charge increases, i.e. the magnetic charge will weaken the absorption capacity of the black hole. Meanwhile, the high-frequency limit of the total absorption cross-section is just the area of black hole shadow.     

Quasinormal Modes of Spherically Symmetric Curve Spacetime with Dark Matter Term

We study quasinormal modes of scalar field perturbation and electromagnetic field perturbation in a black hole space-time with dark matter by using WKB approximation method. The result shows clearly that the real part of black hole quasinormal modes is mainly determined by angular quantum number while its imaginary part mainly determined by model number. We also found out that the dark matter will restrain the perturbation frequency and slow down the speed of damping in spacetime. In addition; dark matter has a greater influence upon quasinormal modes in the electromagnetic field than that in the scalar field.