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.     

Hawking radiation temperatures in non-stationary Kerr black holes with different tortoise coordinate transformations

We apply the Damour–Ruffini–Sannan method to study the Hawking radiations of scalar and Dirac particles in non-stationary Kerr black holes under different tortoise coordinate transformations. We found that all the relevant Hawking radiation spectra show still the blackbody ones, while the Hawking temperatures are strongly related to the used tortoise coordinate transformations. The properties of these dependences are discussed analytically and numerically. Our results imply that proper selections of tortoise coordinate transformations should be important in the studies of Hawking radiations and the correct selection would be given by the experimental observations in the future.     

An interpretation for the entropy of a black hole

We investigate the meaning of the entropy carried away by Hawking radiations from a black hole. We propose that the entropy for a black hole measures the uncertainty of the information about the black hole forming matter’s precollapsed configurations, self-collapsed configurations, and inter-collapsed configurations. We find that gravitational wave or gravitational radiation alone cannot carry all information about the processes of black hole coalescence and collapse, while the total information locked in the hole could be carried away completely by Hawking radiation as tunneling.     

Damour-Ruffini方法和Reissner-Nordstrom黑洞的非热Hawking辐射

利用Damour-Ruffini方法研究了Reissner-Nordstrom黑洞的Hawking辐射，在考虑辐射能量对背景时空反作用的情况下，发现辐射谱不再是理想的热谱. 得到的修正后的Hawking辐射谱，有可能从黑洞中带出信息，进而用来解释黑洞信息丢失佯谬问题，同时满足量子理论的幺正性. 这里的讨论不仅适合于无静止质量的粒子，而且适合于有静止质量的粒子；不仅适合于标量粒子，而且适合于Dirac粒子；具有广泛的适用性.     

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.     

Hawking Radiation via Damour-Ruffini Method in Squashed Charged Rotating Kaluza-Klein Black Holes

Using the Damour-Ruffini method, Hawking radiation of charged particles from squashed charged rotating five-dimensional Kaluza-Klein black holes is investigated extensively. Under the generalized tortoise coordinate transformation, Hawking temperature of the black holes is calculated by using charged scalar particles and Dirac fermions respectively. We find that the obtained Hawking temperature for charged Dirac fermions is the same as for charged scalar particles. What’s more, the spectrum of Hawking radiation contains the information of the size of the extra dimension, which could provide insight for further investigation of large extra dimensions in the future.     

Hawking Radiation as a Possible Probe for the Interior Structure of Regular Black Holes

The notion of black hole singularity and the proof of the singularity theorem were considered great successes in classical general relativity whereas they meanwhile brought with deep puzzles. Conceptual challenges were set up by the intractability of the singularity. The existence of black hole horizons which cover up the black hole interior including the singularity from outside observers, builds an information curtain, further hindering physicists from understanding the nature of the singularity and the interior structure of black holes. The regular black hole is a concept produced out of multiple attempts of establishing a tractable and understandable interior structure for black holes as well as avoiding the singularity behind the black hole horizon. The practicality of the new constructions of black holes would be considered more reliable if there can be found some connection between the interior of regular black holes and some far-reaching signals released from the black hole. After studying the Hawking radiation by fermion tunnelling from one type of regular black hole, structure dependent results were obtained. The result being structure dependent hints the prospects of employing the Hawking radiation as a method to probe into the structure of black holes.     

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.     

Information Loss for QCD Matter in AdS Black Holes at LHC

In this paper, we find the information loss for QCD matter in AdS black holes at LHC by extending the Gottesman and Preskill methode to AdS black holes. We calculate the information transformation from the collapsing matter to the state of outgoing Hawking radiation for both quarks and gluons. It is noticed that for finite values of quark and gluon energies, information from all emission processes experiences some degrees of loss. Possible explanation for this feature will be presented in this paper.     

Information Loss for QCD Matter in AdS Black Holes at LHC

In this paper,we find the information loss for QCD matter in AdS black holes at LHC by extending the Gottesman and Preskill methode to AdS black holes.We calculate the information transformation from the collapsing matter to the state of outgoing Hawking radiation for both quarks and gluons.It is noticed that for finite values of quark and gluon energies,information from all emission processes experiences some degrees of loss.Possible explanation for this feature will be presented in this paper.     

Can Hawking temperatures be negative?

It has been widely believed that the Hawking temperature for a black hole is uniquely determined by its metric and positive. But, I argue that this might not be true in the recently discovered black holes which include the exotic black holes and the black holes in the three-dimensional higher curvature gravities. I argue that the Hawking temperatures, which are measured by the quantum fields in thermal equilibrium with the black holes, might not be the usual Hawking temperature but the new temperatures that have been proposed recently and can be negative. The associated new entropy formulae, which are defined by the first and second laws of thermodynamics, versus the black hole masses show some genuine effects of the black holes which do not occur in the spin systems. Some cosmological implications and physical origin of the discrepancy with the standard analysis are noted also.     

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.     

Hidden messenger revealed in Hawking radiation: A resolution to the paradox of black hole information loss

Using standard statistical method, we discover the existence of correlations among Hawking radiations (of tunneled particles) from a black hole. The information carried by such correlations is quantified by mutual information between sequential emissions. Through a careful counting of the entropy taken out by the emitted particles, we show that the black hole radiation as tunneling is an entropy conservation process. While information is leaked out through the radiation, the total entropy is conserved. Thus, we conclude the black hole evaporation process is unitary.     

Hawking Radiation of Charged Particles via Tunneling from Arbitrarily Dimensional Reissner-Nordström Black Holes

Parikh-Wilzcek’s recent work, which treats the Hawking radiation as semi-classical tunneling process from the event horizon of four dimensional Schwarzshild and Reissner- Nordström black hole, indicates that self-gravitation gives a correction to the Hawking precisely thermal spectrum and the tunneling rate is related to the change of Bekenstein- Hawking, but satisfies the underlying unitary theory. In this paper, we extend the model to study the Hawking radiation of charged particles via tunneling from arbitrarily dimensional Reissner-Nordström black holes, and obtain the same result as Parikh-Wilzcek’s. Meanwhile, in this framework, we point out that the first law of the black hole thermodynamics is reliable and the information conservation is only suitable for the reversible process.     

The information paradox: Conflicts and resolutions

Many relativists have been long convinced that black hole evaporation leads to information loss or remnants. String theorists have however not been too worried about the issue, largely due to a belief that the Hawking argument for information loss is flawed in its details. A recently derived inequality shows that the Hawking argument for black holes with horizon can in fact be made rigorous. What happens instead is that in string theory, black hole microstates have no horizons. Thus the evolution of radiation quanta with E??kT is modified by order unity at the horizon, and we resolve the information paradox.     

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.     

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.     

Horned particles as the endpoint of Hawking evaporation

This essay reviews recent developments in the theory of Hawking evaporation of black holes. Study of near extremal magnetically charged black holes using a two plus four dimensional effective field theory has led to the concept of horned particles orcornucopion as the endpoint of Hawking evaporation. Horned particles are geometries containing two large asymptotic regions connected by microscopic necks. They look like point particles to an observer in any given asymptotic region, but in many ways behave like macroscopic objects. In particular, it is very difficult to pair produce them in external fields and their contribution to virtual loops is highly suppressed. They can serve as the remnants necessary to account for the information apparently lost in Hawking evaporation. The information simply goes into the new asymptotic region formed when the black hole collapses and evaporates.This essay received the second award from the Gravity Research Foundation, 1993-Ed.     

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.