Dirac Particles＇ Hawking Radiation from a Schwarzschild Black Hole

Considering energy conservation and the backreaction of particles to spacetime, we investigate the massless/massive Dirac particles＇ Hawking radiation from a Schwarzschild black hole, The exact expression of the emission rate near the horizon is obtained and the result indicates that Hawking radiation spectrum is not purely thermal. The result obtained is consistent with the results obtained before. It satisfies the underlying unitary theory and offers a possible mechanism to explain the information loss paradox. Whereas the improved Damour-Rufflni method is more concise and understandable,     

Statistical-Mechanical Entropies of Schwarzschild Black Hole due to Arbitrary Spin Fields in Different Coordinates

The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita-Schwinger and gravitational fields are investigated in the Painlevg and Lemaitre coordinates. Although the metrics in the Painlevg and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painlevd and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild coordinate.     

Canonical Entropy and Phase Transition of Rotating Black Hole

Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Havcking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.     

Quasinormal Spectrum and Quantization of the Kerr--Newman Black Hole

The intermediate asymptotic quasinormal mode spectrum of the charged scalar and Dirac fields in the near extremal Kerr-Newman black hole is studied analytically, It is found that the quasinormal mode spectrum can be expressed in terms of the Hawking temperature Thb, the electric potential Ф＋ and the horizon＇s angular velocity ΩH for the case of （eФ_ ＋ mΩH） 〉 （1 - 4πThb）Re（ω） （where e is the charge and m is the azimuthal projection number）, whereas it is only relevant to the charge and the mass parameter for another case. It is also shown that by using the Bohr＇s correspondence principle, the fundamental change in the black-hole surface area induced by the emission of a rotating charged quantum from the Kerr-Newman black hole is in accord with the Bekenstein-Mukhanov general prediction.     

Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole

A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli （BTZ） black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS＋ Pr dA, where E = M is the mass of BTZ black hole, dA is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, Pr is the radial pressure provided by the source of Einstein equations, S = 41πa is the entropy and T =κ/2π is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole, showing that it is also possible to interpret the field equation near horizon as a thermodynamic identity dE = TdS ＋ PrdA ＋Ω＋dJ, where Ω＋ is the angular velocity and J is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near the horizon.     

Massive Particle＇s Tunnelling from Black Hole with Topological Defect

We extend Zhang and Zhao＇s recent work to black hole with topological defect whose Arnowitt-Deser-Misner mass is no longer identical to its mass parameter. The behaviour of the tunnelling massive particles is investigated, and the emission rate at which massive particles tunnel across the event horizon of the black hole is calculated. The result is consistent with an underlying unitary theory, and takes the same functional form as that of mass-less particles.     

Entropy corrections for Schwarzschild black holes

Recently it is shown that the Bekenstein–Hawking entropy for black holes receives logarithmic corrections due to thermodynamic fluctuations. Schwarzschild black hole which possesses a negative specific heat is thermodynamically unstable, so the entropy corrections cannot be obtained directly. In this Letter, Schwarzschild black hole will be put in the center of a spherical cavity of finite radius to achieve equilibrium with surroundings, so that a thermodynamically stable solution is obtained based on a uniformly spaced area spectrum approach. Our conclusion show that there are two correction terms for Schwarzschild black holes. The sign of the second correction term depends on the size of the cavity.     

Brick Wall Model and the Spectrum of a Schwarzschild Black Hole

The quantum entropy of a scalar field near a Schwarzschild black hole is investigated by employing the brick-wall model in the grand canonical ensemble. A positive chemical potential is introduced if the cutoff is set to be of order of the Planck length. We also discuss the relation between the chemical potential and the mass quantum of the black hole.     

Statistical-Mechanical Entropy of a Black Hole with a Global Monopole to All Orders in Planck Length

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle, we calculate the statistical entropy of the scalar field in the global monopole black hole spacetime without any artificial cutoff. It is shown that the entropy is proportional to the horizon area.     

Charged Particle Tunnels from the Slowly Varying Reissner-Nordstroem Black Hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we discuss the Hawking radiation of the slowly varying Reissner-NordstrSm black hole by considering the unfixed background spacetime and the selfgravitation interaction. The result shows that the tunnelling rate is related to both the variation of BekensteinHawking entropy and the radiation spectrum deviating from the purely thermal one. This is in agreement with Parikh and Wilczek＇s result. Then a new method to study Hawking radiation of the non-stationary black holes is presented.     

A New Method to Study Hawking Radiation of Charged Particle from Stationary Axisymmetric Sen Black Hole

Taking the self-gravitation interaction and energy conservation,charge conservation and angular momentum conservation into accpunt, we discuss the tunnelling characteristics of the charged particle from Sen black hole by the Hamilton-Jacobi method. The result shows that the tunnelling probability is related to the change of Bekenstein-Hawking entropy, and the actual radiation spectrum deviates from the pure thermal one, which is consistent with the result of Parikh and Wilczek and gives a new method to correct the Hawking pure thermal spectrum of Sen black hole.     

Hawking Radiation from Topological Kerr Anti-de-Sitter Black Hole with One Rotational Parameter via Covariant Anomalies

Using anomalous viewpoint, we study the Hawking radiation from a kind of topological Kerr Anti-de-Sitter （Kerr-AdS） black hole with one rotational parameter. We employ the covariant gauge and gravitational anomalies. The result supports the Robinson-Wilczek opinion and shows that the Hawking temperature can be correctly determined by cancelling covariant gauge and gravitational anomalies at the horizon.     

Geodesics of Spherical Dilaton Spacetimes

The properties of spherical dilaton black hole spacetimes are investigated through a study of their geodesics. The closed and non-closed orbits of test particles are analysed using the effective potential and phase-plane method. The stability and types of orbits are determined in terms of the energy and angular momentum of the test particles. The conditions of the existence of circular orbits for a spherical dilaton spacetime with an arbitrary dilaton coupling constant α are obtained. The properties of the orbits and in particular the position of the innermost stable circular orbit are compared to those of the Reissner-Nordstrom spacetime. The circumferential radius of innermost stable circular orbit and the corresponding angular momentum of the test particles increase for α≠ 0.     

Viscous Cosmology and Thermodynamics of Apparent Horizon

It is shown that the differential form of Friedmann equations of Friedman--Robertson--Walker (FRW) universe can be recast as a similar form of the first law T_hdS_h = dE + WdV of thermodynamics at the apparent horizon of FRW universe filled with the viscous fluid. It is also shown that by employing the general expression of temperature associated with the apparent horizon of an FRW universe and assumed that the temperature T_m of the energy inside the apparent horizon is proportional to the horizon temperature T_m= bT_h, we are able to show that the generalized second law of thermodynamics holds in the Einstein gravity provided T_h-T_m/r^~_A ≤(ρ+P^~).     

Gauss-Bonnet and Lovelock Gravities and the Generalized Second Law of Thermodynamics

It has been shown [Chin. Phys. Lett.25 （2008） 4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss-Bonnet and Lovelock gravities. It is shown that by employing the general expression for temperature Th =｜κ｜/2π= 1/2πτA （1-τA/2HτA） associated with the apparent horizon of a Friedman Robertson-Walker （FRW） universe and assuming Tm = bTh, we are able to construct conditions for which the generalized second law holds in Gauss Bonnet and Lovelock gravities, where Tm and Th are the temperatures of the source and the horizon respectively.     

Generalized Uncertainty Principle and the Quantum Entropy of Rotating Black Hole

The entropy of rotating Kerr-Newman-Kasuya black hole due to massive charged fields （bosons and fermions） is calculated by using the new equation of state density motivated by the generalized uncertainty relation. The result shows the entropy does not depend on the mass and the charge but the parameter A, the area A and the spin of the fields. Moreover, an improved approximation is provided to calculate the scalar entropy.     

Tunnelling Effect and Hawking Radiation from a Vaidya Black Hole

We extend Parikh＇s study to the non-stationary black hole. As an example of the non-stationary black hole, we investigate the tunnelling effect and Hawking radiation from a Vaidya black hole whose Bondi mass is identical to its mass parameter. The Hawking radiation is considered as a tunnelling process across the event horizon and we calculate the tunnelling probability. It is found that the is the function of Bondi mass re（υ）. result is different from Parikh＇s study because dr H/dυ     

Late-Time Evolution of the Phantom Scalar Perturbation in the Background of a Spherically Symmetric Static Black Hole

The late-time evolution of the phantom scalar perturbation is investigated in the spacetime of a four-dimensionai spherically symmetric static black hole. It is revealed that the asymptotic tail of the phantom scalar field is dominated by the growth behavior t-（l＋3/2）eμt, which depends on the multipole moment l and the field moss but is independent of the mass M and charge Q of the black hole. This growth behavior is in strong contrast to the decaying tall of the usual massive scalar perturbation and shows that the external phantom scalar perturbation is unstable in the spherically symmetric static black hole spacetime.     

Tunnelling Effect of Two Horizons from a Gibbons--Maeda Black Hole

We study the thermal characters of the inner horizon of a Gibbons-Maeda black hole. In order to satisfy the Nernst theorem of the third law, the entropy of the black hole with two horizons must depend not only on the area of the outer horizon but also on the area of the inner horizon. Then the temperature of the inner horizon is calculated. Lastly, the tunnelling effect including the inner horizon of a Gibbons-Maeda black hole is investigated. We also calculate the tunnelling rate of the outer horizon Г＋ and the inner horizon Г_. The total tunnelling rate Г should be the product of the rates of the outer and inner horizon, Г =Г＋ · Г_. It is found that the total tunnelling rate is in agreement with the Parikh＇s standard result, Г→ exp（ ASBH ）, and there is no information loss.     

Quasinormal modes of black holes absorbing dark energy

We study perturbations of black holes absorbing dark energy. Due to the accretion of dark energy, the black hole mass changes. We observe distinct perturbation behaviors for absorption of different forms of dark energy onto the black holes. This provides the possibility of extracting information whether dark energy lies above or below the cosmological constant boundary w=−1$w=-1$. In particular, we find in the late time tail analysis that, differently from the other dark energy models, the accretion of phantom energy exhibits a growing mode in the perturbation tail. The instability behavior found in this work is consistent with the Big Rip scenario, in which all of the bound objects are torn apart with the presence of the phantom dark energy.