Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Recently,considerable progress has been made in understanding the early universe by loop quantum cosmology.Modesto et al.investigated the loop quantum black hole(LQBH)using improved semiclassical analysis and they found that the LQBH has two horizons,an event horizon and a Cauchy horizon,just like the Reissner-Nordstr¨om black hole.This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background.By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method,we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly.However,the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value.We also find that the loop quantum gravity area gap parameter a 0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer.In the complex ω plane,the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.     

Quasinormal Modes of the Planar Black Holes of a Particular Lovelock Theory

In this work, we study the scalar quasinormal modes of a planar black hole metric in asymptotic anti-de Sitter spacetime derived from a particular Lovelock theory. The quasinormal frequencies are evaluated by adopting the Horowitz-Hubeny method as well as a matrix formalism. Also, the temporal evolution of small perturbations is studied by using finite difference method. The roles of the dimension of the spacetime, the parameter of the metric k, as well as the temperature of the background black hole, are discussed. It is observed that the particular form of the metric leads to quasinormal frequencies whose real parts are numerically insignificant. The black hole metric is found to be stable against small scalar perturbations.     

Massive scalar field quasinormal modes of a Schwarzschild black hole surrounded by quintessence

We present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field u plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass of the field u increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly than the massless scalar field. The frequencies have a limited value, so it is easier to detect the quasinormal modes. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.      

Massive Quasinormal Modes of a Schwarzschild-de Sitter Black Hole with a Global Monopole

Using the WKB approximation, we evaluate both the massless and massive scalar and Dirac fields quasinormal modes (QNMs) of a Schwarzschild-de Sitter black hole. The result shows that the field with higher masses and larger cosmological constant λ will decay more slowly. We also found that the global monopole is similar to a factor to modify the κ of Dirac field or l of scalar field, where κ is the angular momentum number of Dirac field, and l is the angular momentum number of scalar field.     

“Charged” particle’s tunneling from rotating black holes

The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from rotating black hole can be treated as “charged” particle’s tunneling process in its effectively two dimensional metric. Using this viewpoint and considering the corresponding “gauge charge” conservation, we calculate the non-thermal tunneling rate of Kerr black hole and Myers–Perry black hole, and results are consistent with Parikh–Wilczek’s original result for spherically symmetric black holes. Especially for Myers–Perry black hole which has multi-rotation parameters, our calculation fills in the gap existing in the literature applying Parikh–Wilczek’s tunneling method to various types black holes. Our derivation further illuminates the essential role of effective gauge symmetry in Hawking radiation from rotating black holes.     

Slowly rotating charged black holes in anti-de Sitter third order Lovelock gravity

In this paper, we study slowly rotating black hole solutions in Lovelock gravity (n = 3). These solutions are obtained in uncharged and charged cases, respectively. Up to the linear order of the rotating parameter a, the entropy and gyromagnetic ratio of black holes keep invariant after introducing the Gauss-Bonnet and third order Lovelock interactions.     

Greybody factors of charged dilaton black holes in 2 + 1 dimensions

We have studied the scalar perturbation of charged dilaton black holes in 2+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2+1 dimensions. The exact decay rates and the grey body factors for the massless minimally coupled scalar is computed for both the charged and the uncharged dilaton black holes. The charged and the uncharged black hole show similar behavior for grey body factors, reflection coefficients and decay rates.This revised version was published online in April 2005. The publishing date was inserted.     

Free energy of a Lovelock holographic superconductor

We study thermodynamics of black hole solutions in Lanczos–Lovelock anti-de Sitter gravity in \(d+1\) dimensions coupled to nonlinear electrodynamics and a Stückelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in \(d\) dimensions. A larger number of coupling constants in the gravitational side is necessary to widen the domain of validity of physical quantities in dual quantum field theory (QFT). We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and we obtain the exact formula for the free energy of the superconductor in the holographic QFT. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.     

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.     

A new metric for rotating black holes in Gauss-Bonnet gravity

This paper presents a new metric and studies slowly rotating Gauss-Bonnet black holes with a nonvanishing angular momentum in five dimensional anti-de Sitter spaces.Taking the angular momentum parameter a up to second order,the slowly rotating black hole solutions are obtained by working directly in the action.In addition,it also finds that this method is applicable in higher order Lovelock gravity.     

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.     

Evolution of massive scalar fields in the spacetime of a tense brane black hole

In the spacetime of a d-dimensional static tense brane black hole we elaborate the mechanism by which massive scalar fields decay. The metric of a six-dimensional black hole pierced by a topological defect is especially interesting. It corresponds to a black hole residing on a tensional 3-brane embedded in a six-dimensional spacetime, and this solution has gained importance due to the planned accelerator experiments. It happened that the intermediate asymptotic behaviour of the fields in question was determined by an oscillatory inverse power-law. We confirm our investigations by numerical calculations for five- and six-dimensional cases. It turned out that the greater the brane tension is, the faster massive scalar field decay in the considered spacetimes.     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

Geometric Character of Black-Hole Entropy

The geometry of the neighborhood near an event horizon is similar to the Rindlermetric, which leads to the thermal effect of black holes. The entropy of the scalarfield and the Dirac field are calculated in the black-hole background. The entropyof the scalar field, which is proportional to the area of the event horizon, isnaturally derived. Under the condition of large-mass black hole, the entropy ofthe Dirac field is still proportional to the area of the horizon. These results canbe applied to a large class of black holes. A new method for calculating the blackhole entropy is proposed which makes it easy to calculate the entropy of ahigh-spin field in the black-hole background. We also consider extreme black holesand point out that the topological entropy only has classical meaning.     

Scalar field coupling to Einstein tensor in regular black hole spacetime

In this paper, we study the perturbation property of a scalar field coupling to Einstein’s tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant \(\eta \) imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein’s tensor in the regular black hole spacetimes by the 3rd order WKB method.     

Scalar field dynamics in warped AdS3 black hole background

We study the normal modes of a scalar field in the background of a warped AdS₃ black hole which arises in topologically massive gravity. We discuss the normal mode spectrum using the brick wall boundary condition. In addition, we investigate the possibility of a more general boundary condition for the scalar field.     

Hawking radiation and tunneling mechanism for a new class of black holes in Einstein–Gauss–Bonnet gravity

We study Hawking radiation in a new class of black hole solutions in Einstein–Gauss–Bonnet theory. The black hole has been argued to have vanishing mass and entropy, but finite Hawking temperature. To check if it really emits radiation, we analyze Hawking radiation using the original method of quantization of a scalar field in the black hole background and with the quantum tunneling method, and confirm that it emits radiation at the Hawking temperature. A general formula is derived for the Hawking temperature and backreaction in the tunneling approach. Physical implications of these results are discussed.     

Quasi-normal Modes of AdS5 Black Hole at $\mathcal{N}=2$ Supergravity

In this paper we consider the AdS ₅ black hole at the \(\mathcal{N}=2\) supergravity background. By using the AdS/CFT correspondence we discuss about the quasi-normal modes of the scalar field in the black hole, which is dual of the scalar glueballs spectrum on the boundary. We obtain phase transition conditions from stable to unstable theory, which interpreted as confinement and deconfinement states in the QCD. We obtain the specific heat in terms of the temperature and charge of black hole, we find the temperature where the black hole is stable. Also we rewrite the equation of motion in the Schrödinger form and discuss the effective potential.     

Reissner-Nordstrom几何中标量场的统计熵与能斯特定理

从Reissner-Nordstrom时空背景下的Klein-Gordon方程出发,利用改进的brick-wall方法膜模型,计算黑洞背景下标量场的自由能和熵.得到标量场的熵是由两部分组成的,根据熵是广延量的性质,得到黑洞熵是由两个子热力学系统贡献的.在此基础上给出了新的Bekenstein-Smarr公式.结果表明,用两个子热力学系统表达的熵,当黑洞的辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵. 关键词： brick-wall方法 膜模型 黑洞熵 能斯特定理     

Hawking radiation from a five-dimensional Lovelock black hole

We investigate Hawking radiation from a five-dimensional Lovelock black hole using the Hamilton–Jacobi method. The behavior of the rate of radiation is plotted for various values of the ultraviolet correction parameter and the cosmological constant. The results show that, owing to the ultraviolet correction and the presence of dark energy represented by the cosmological constant, the black hole radiates at a slower rate in comparison to the case without ultraviolet correction or cosmological constant. Moreover, the presence of the cosmological constant makes the effect of the ultraviolet correction on the black hole radiation negligible.