Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner–Nordström black hole, the Kerr black hole, and the Kerr–Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.     

Tunneling Radiation of Massive Vector Bosons from Dilaton Black Holes

It is well known that Hawking radiation can be treated as a quantum tunneling process of particles from the event horizon of black hole. In this paper, we attempt to apply the massive vector bosons tunneling method to study the Hawking radiation from the non-rotating and rotating dilaton black holes. Starting with the Proca field equation that govern the dynamics of massive vector bosons, we derive the tunneling probabilities and radiation spectrums of the emitted vector bosons from the static spherical symmetric dilatonic black hole, the rotating Kaluza-Klein black hole, and the rotating Kerr-Sen black hole. Comparing the results with the blackbody spectrum, we satisfactorily reproduce the Hawking temperatures of these dilaton black holes, which are consistent with the previous results in the literature.     

Charged Fermions Tunneling from a Rotating Charged Black Hole in 5-Dimensional Gauged Supergravity

Recent research shows that Hawking radiation from black hole horizoncan be treated as a quantum tunneling process, and fermions tunneling method can successfully recover Hawking temperature. In this tunneling framework, choosing a set of appropriate matrices γ^μ is an important technique for fermions tunneling method. In this paper, motivated by Kerner and Man's fermions tunneling method of 4 dimension black holes, we further improve the analysis to investigate Hawking tunneling radiation from a rotating charged black hole in 5-dimensional gauged supergravity byconstructing a set of appropriate matrices γ^μ for general covariant Dirac equation. Finally, the expected Hawking temperature of the black hole is correctly recovered, which takes the same form as that obtained by other methods. This method is universal, and can also be directly extend to the other different-type 5-dimensional charged black holes.     

Hawking radiation and page curves of the black holes in thermal environment

As realistic objects in the Universe, the black holes are surrounded by complex environment. By taking the effect of thermal environment into account, we investigate the evaporation process and the time evolutions (page curves) of the entanglement entropies of Hawking radiation of various types of black holes. It is found that the black holes with the thermal environments evaporate slower than those without the environments due to the environmental contribution of the energy flux in addition to Hawking radiation. For Schwarzschild black hole and Reissner-Nordström black hole in flat spaces, when the initial temperature of the black hole is higher than the environment temperature, the black holes evaporate completely and the Hawking radiation is eventually purified. For Schwarzschild-AdS black hole, it will evaporate completely and the Hawking radiation is purified when the environment temperature is lower than the critical temperature. Otherwise, it will reach an equilibrium state with the environment and the radiation is maximally entangled with the black hole. Our results indicate that the final state of the black hole is determined by the environmental temperature and the temporal evolution and the speed of the information purification process characterized by the page curve of the Hawking radiation is also influenced by the thermal environment significantly.     

Charged fermions tunneling from regular black holes

We study Hawking radiation of charged fermions as a tunneling process from charged regular black holes, i.e., the Bardeen and ABGB black holes. For this purpose, we apply the semiclassical WKB approximation to the general covariant Dirac equation for charged particles and evaluate the tunneling probabilities. We recover the Hawking temperature corresponding to these charged regular black holes. Further, we consider the back-reaction effects of the emitted spin particles from black holes and calculate their corresponding quantum corrections to the radiation spectrum. We find that this radiation spectrum is not purely thermal due to the energy and charge conservation but has some corrections. In the absence of charge, e = 0, our results are consistent with those already present in the literature.     

Fermions Tunneling Mechanism for a New Class of Black Holes in EGB Gravity and Three-Dimensional Lifshitz Black Hole

The objective of this paper is to investigate the Fermions tunneling radiation of a new class of black holes in Einstein-Gauss-Bonnet (EGB) gravity and three-dimensional Lifshitz black hole in New Massive Gravity (NMG). As a result, the tunneling probability and Hawking temperature of the black holes are well recovered, which confirms that the Hawking temperature of emitted Dirac particles of the black holes are the same as in the case of scalar particles. The quantization of entropy from the black hole have also been discussed.     

Covariant anomalies and Hawking radiation from Kaluza–Klein AdS black holes

In this paper, Hawking radiation is studied from four-dimensional (4D) Kaluza–Klein (KK) AdS black holes via the method of anomaly cancellation. The KK-AdS black hole considered is a non-extremal charged rotating solution in the theory of 4D gauged supergravity. Its Hawking fluxes of electric charge, angular momentum and energy momentum tensor are derived here. Our results support the common view that Hawking radiation is the quantum effect arising at the event horizon.     

Fermions tunnelling from the rotating 5-D Myers–Perry black hole

Recent researches on the Hawking radiation of black holes show that the Hawking temperature can be obtained by fermion tunnelling method. In this paper, we extend this method to a 5-D space-time and view the Hawking radiation of the Myers–Perry black hole with two independent angular momenta. As a result, the Hawking temperature is obtained, which is the same as that obtained by other methods.     

Thermodynamics of rotating regular black holes

This paper presents a study on the thermodynamics of rotating Bardeen as well as Hayward regular black hole and their anti-de Sitter versions. We analyze the temperature, entropy, heat capacity and thermodynamical stability for the considered black hole geometries. The Hawking temperature is calculated using the surface gravity as well as tunneling probability method leading to the same result. We conclude that the considered rotating as well as rotating anti-de Sitter regular black holes are less hot and thermodynamically more stable than ordinary Kerr and Kerr-anti-de Sitter solutions, respectively.     

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordström black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.     

Hawking Radiation from Plane Symmetric Black Hole Covariant Anomaly

Based on the covariant anomaly cancellation method, which is believed to be more refined than the initial approach of Robinson and Wilczek, we discuss Hawking radiation from the plane symmetric black hole. The result shows that Hawking radiation from the non-spherical symmetric black holes also can be derived from the viewpoint of anomaly.     

One-Dimensional Quantum Channel and Hawking Radiation of Kerr and Kerr-Newman Black Holes

In this paper, we review the one-dimensional quantum channel and investigate Hawking radiation of bosons and fermions in Kerr and Kerr-Newman black holes. The result shows the Hawking radiation can be described by the quantum channel. The thermal conductances are derived and related to the black holes’ temperatures. The electric conductance of the Kerr-Newman black hole is obtained and only related to the charge of emission particles.     

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 $b$.     

Charged particle tunnels from the stationary and non-stationary Kerr–Newman black holes

Considering the unfixed background space-time and self-gravitational interaction, we view the Hawking radiation of a stationary Kerr–Newman black hole by Hamilton–Jacobi method. Meanwhile, extending this work to non-stationary black holes, we attempt to investigate the Hawking radiation of the non-stationary Kerr–Newman black hole. Both of the results show the tunneling probabilities are related to the change of Bekenstein- Hawking entropy and the radiation spectrums deviate from the purely thermal one, which is in accordance with the known result.     

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 simpler method for researching fermions tunneling from black holes

A new simpler mathematic method is proposed to study fermions tunneling from black holes. According to this method, by using semiclassical approximation theory, it simplifies the Dirac equation of curved spacetime and then the relationship of the gamma matrix and the component of contravariant metric is considered in order to transform the set of difficult quantum equations into a simple equation. Finally, the fermion tunneling and Hawking radiation of black holes are obtained. The method is very effective and simple, and we will take the Schwarzschild black hole with global monopole and the higher-dimensional Reissner-Nordstrom de Sitter black hole as two examples to show the fact.     

Collision of two rotating Hayward black holes

We investigate the spin interaction and the gravitational radiation thermally allowed in a head-on collision of two rotating Hayward black holes. The Hayward black hole is a regular black hole in a modified Einstein equation, and hence it can be an appropriate model to describe the extent to which the regularity effect in the near-horizon region affects the interaction and the radiation. If one black hole is assumed to be considerably smaller than the other, the potential of the spin interaction can be analytically obtained and is dependent on the alignment of angular momenta of the black holes. For the collision of massive black holes, the gravitational radiation is numerically obtained as the upper bound by using the laws of thermodynamics. The effect of the Hayward black hole tends to increase the radiation energy, but we can limit the effect by comparing the radiation energy with the gravitational waves GW150914 and GW151226.     

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.     

Fermions Tunnelling with Quantum Gravity Correction

Based on the generalized uncertainty principle (GUP), we investigate the correction of quantum gravity to Hawking radiation of black hole by utilizing the tunnelling method. The result tells us that the quantum gravity correction retards the evaporation of black hole. Using the corrected covariant Dirac equation in curved spacetime, we study the tunnelling process of fermions in Schwarzschild spacetime and obtain the corrected Hawking temperature. It turns out that the correction depends not only on the mass of black hole but also on the mass of emitted fermions. In our calculation, the quantum gravity correction slows down the increase of Hawking temperature during the radiation explicitly. This correction leads to the remnants of black hole and avoids the evaporation singularity.