The temperature in Hawking radiation as tunneling

The quasi-classical method of deriving Hawking radiation under the consideration of canonical invariance is investigated. We find that the horizon should be regarded as a two-way barrier and the ingoing amplitude should be calculated according to the negative energy particles tunneling into the black hole because of the whole space–time interchange and thus the standard Hawking temperature is recovered. We also discuss the advantage of the Painlevé coordinates in Hawking radiation as tunneling.     

Eruptive Massive Vector Particles of 5-Dimensional Kerr-Gödel Spacetime

In this paper, we investigate Hawking radiation of massive spin-1 particles from 5-dimensional Kerr-Gödel spacetime. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the relativistic Proca equation, we obtain the quantum tunneling rate of the massive vector particles. Using the obtained tunneling rate, we show how one impeccably computes the Hawking temperature of the 5-dimensional Kerr-Gödel spacetime.     

Hawking Temperature Calculation Using Tunneling Mechanism

Based on the black hole tunneling mechanism in which the ingoing particles should be absorbed absolutely, Hamilton-Jacobi method is modified to investigate Hawking radiation from a Schwarzschild black hole once again. The results are independent on the coordinates and the standard Hawking temperature is obtained without the factor of 2 problem. Moreover, it is also pointed out that the modified Hamilton-Jacobi method can be applied to investigate Hawking radiation from the general horizons in dynamical spacetimes.     

Which coordinate representations can give correct Hawking temperature of Kerr black hole by tunneling approach

Some authors found that, in different coordinates, the tunneling approach gives different Hawking temperature for the Schwarzschild black hole recently. In this paper, by studying the Hawking radiation of the Kerr black hole arising from the scalar and Dirac particles, we find that, to obtain the Hawking temperature by using tunneling effect, the coordinate representations for the stationary Kerr black hole should satisfy two conditions: (a) to keep the Killing vectors x_(t)^m{{\xi_{(t)}^\mu}} and x_(j)^m{{\xi_{(\varphi)}^\mu}} invariant; and (b) the radial coordinate transformation is a regular and non-zero function.     

Hawking Radiation of Grumiller Black Hole

In this paper, we consider the relativistic Harnilton-Jacobi （HJ） equation and study Hawking radiation （HR） of scalar particles from uncharged Grumiller black hole （GBH） which is affordable for testing in astrophysics. It is a/so known as Rindler modified Schwarzschild BH. Our aim is not only to investigate the effect of the Rindler parameter a on the Hawking temperature （TH ）, but to examine whether there is any discrepancy between the computed horizon temperature and the standard TH as well. For this purpose, in addition to its naive coordinate system, we study on the three regular coordinate systems, which are Painlevd--Gullstrand （PG）, ingoing Edding~on-Finkelstein （IEF）, and Kruskal-Szekeres （KS） coordinates. In o21 coordinate systems, we calculate the tunneling probabilities of incoming and outgoing scalar particles from the event horizon by using the HJ equation. It has been shown in detail that the considered HJ method is concluded with the conventional T~ in all these coordinate systems without giving rise to the famous factor-2 problem. Filrthermore, in the PG coordinates Parikh-Wilczek＇s tunneling （PWT） method is employed in order to show how one can integrate the quantum gravity （QG） corrections to the semiclassical tunneling rate by including the effects of self-gravitation and back reaction. We then show how this yields a modification in the TH.     

Tunneling Radiation of Vector Particles from a Quantum Correction Black Hole

The purpose of this paper is to discuss the Hawking radiation of vector particles from a quantum correction black hole by the mean of quantum tunneling. In order to achieve this purpose, based on the Proca field equation and WKB approximation, the quantum tunneling method is used to calculate the tunneling rate and Hawking temperature of the black hole. According to the analysis of the consequences, we find that the tunneling rate and Hawking temperature are related to the quantum parameter besides the horizon radius and mass of the black hole. Furthermore, when the results are compared with those of scalar particles and fermions of the black hole, no difference is found. Therefore, the tunneling rate and Hawing temperature of the black hole do not change with the type of radiation particles.

     

Dirac Particles' Tunneling Radiation from Dilaton Space-time with Squashed Horizons

The aim of this paper is to investigate Hawking radiation of Dirac particles from the Dilaton space-time with squashed horizons by improving the method of Kerner and Man's tunneling analysis. We construct appropriate matrices for general covariant Dirac equation, and derive the tunneling probability and Hawking temperature. The results show that both Dirac particles and scalar particles radiate at the same Hawking temperature.     

Effect of the refractive index on the hawking temperature: an application of the Hamilton-Jacobi method

Hawking radiation of a non-asymptotically flat 4-dimensional spherically symmetric and static dilatonic black hole (BH) via the Hamilton-Jacobi (HJ) method is studied. In addition to the naive coordinates, we use four more different coordinate systems that are well-behaved at the horizon. Except for the isotropic coordinates, direct computation by the HJ method leads to the standard Hawking temperature for all coordinate systems. The isotropic coordinates allow extracting the index of refraction from the Fermat metric. It is explicitly shown that the index of refraction determines the value of the tunneling rate and its natural consequence, the Hawking temperature. The isotropic coordinates in the conventional HJ method produce a wrong result for the temperature of the linear dilaton. Here, we explain how this discrepancy can be resolved by regularizing the integral possessing a pole at the horizon.     

Particles’ Tunneling in Spherically Symmetric Spacetimes with Dark Matter

Applying the Hamilton-Jacobi method, we investigate particles’ tunneling behavior in a spherically symmetric spacetime with dark matter. The tunneling rate and Hawking temperature at the event horizon are obtained. The result shows that the dark matter parameter β has an important influence on the Hawking temperature and the tunneling rate.     

Hawking radiation of spin-1 particles from a three-dimensional rotating hairy black hole

We study the Hawking radiation of spin-1 particles (so-called vector particles) from a three-dimensional rotating black hole with scalar hair using a Hamilton–Jacobi ansatz. Using the Proca equation in the WKB approximation, we obtain the tunneling spectrum of vector particles. We recover the standard Hawking temperature corresponding to the emission of these particles from a rotating black hole with scalar hair.     

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.     

Entangled Particles Tunneling From a Schwarzschild Black Hole immersed in an Electromagnetic Universe with GUP

Quantum gravity has exciting peculiarities on the Planck scale.The effect of generalized uncertainty principle (GUP) to the entangled scalar/fermion particles’ tunneling from a Schwarzschild black hole immersed in an electromagnetic Universe is investigated by the help of semi-classical tunneling method. The quantum corrected Hawking temperature of this black hole with an external parameter “a” modifies the Hawking temperature for the entangled particles.     

Hawking radiation of Dirac particles from soft-hairy black holes

In this paper, we study the Hawking radiation of Dirac particles via tunneling formalism from linearly supertranslated Schwarzschild black holes. We find that the radiation spectrum and the Hawking temperature remain the same as the one without soft hair.     

Fermion tunneling from a non-static black hole with the internal global monopole

Kerner and Mann’s recent research shows that the Hawking temperature and tunneling rate can be obtained by the fermion tunneling method from the Rindler space-time and a general non-rotating black hole. In this paper, considering the tunneling particles with spin 1/2 and taking into account the particle’s self-gravitation in the dynamical background space-time, we further improve Kerner and Man’s fermion tunneling method to investigate Hawking radiation via tunneling from a non-static black hole with the internal global monopole. The result shows that the tunneling rate of the non-static black hole is related to the integral of the changing horizon besides the change of Bekenstein–Hawking entropy, which is different from the stationary cases. It also essentially implies that the unitary is violated for the reason that the black hole is non-stationary and cannot be treated as an isolated system.     

Tunneling of massive particles from noncommutative inspired Schwarzschild black hole

We apply the generalization of the Parikh–Wilczek method to the tunneling of massive particles from noncommutative inspired Schwarzschild black holes. By deriving the equation of radial motion of the tunneling particle directly, we calculate the emission rate which is shown to be dependent on the noncommutative parameter besides the energy and mass of the tunneling particle. After equating the emission rate to the Boltzmann factor, we obtain the modified Hawking temperature which relates to the noncommutativity and recovers the standard Hawking temperature in the commutative limit. We also discuss the entropy of the noncommutative inspired Schwarzschild black hole and its difference after and before a massive particle’s emission.     

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.     

Massive Vector Particles Tunneling from the Neutral Rotating Anti-de Sitter Black Holes in Conformal Gravity

We investigate the massive vector particles' Hawking radiation from the neutral rotating Anti-de Sitter(AdS) black holes in conformal gravity by using the tunneling method.It is well known that the dynamics of massive vector particles are governed by the Proca field equation.Applying WKB approximation to the Proca equation,the tunneling probabilities and radiation spectrums of the emitted particles are derived.Hawking temperature of the neutral rotating AdS black holes in conformal gravity is recovered,which is consistent with the previous result in the literature.     

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.     

Tunneling effect of Dirac particles from the non-extremal black hole in <Emphasis Type="Italic">D</Emphasis> = 5, <Emphasis Type="Italic">SO</Emphasis>(6) gauged supergravity

Recent research shows that Hawking radiation from black hole horizon can 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 the non-extremal black hole in D = 5, SO(6) gauged supergravity by constructing 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.     

Hawking radiation in the spacetime of white holes

A white hole (WH) is a time-reversed black hole (BH) solution in general relativity with a spacetime region to which cannot be entered from the outside. Recently they have been proposed as a possible solution to the information loss problem (Haggard et al. in Phys Rev D 92:104020, 2015). In particular it has been argued that the quantization of the gravitational field may prevent a BH from collapsing entirely with an exponential decay law associated to the black-hole-to-white-hole (BHWH) tunneling scenario (Barcelo et al. in Class Quantum Gravit 34:105007, 2017). During this period of BHWH transition the Hawking radiation should take place. Taking this possibility into account, we utilize the Hamilton–Jacobi and Parkih–Wilczek methods to study the Hawking radiation viewed as a quantum tunneling effect to calculate the tunneling rate of vector particles tunneling inside (outside) the horizon of a WH (BH), respectively. We show that there is a Hawking radiation associated to a WH spacetime equal to the BH Hawking temperature when viewed from the outside region of the WH geometry. In the framework of Parkih–Wilczek method, surprisingly, we show that Hawking temperature is affected by the initial radial distance at which the gravitational collapse starts.