Parikh Wilczek Tunneling Framework Research Articles

Hawking radiation and entropy of a black hole in Lovelock-Born-Infeld gravity from the quantum tunneling approach**Supported by Guangdong Natural Science Foundation (2016A030307051, 2015A030313789)

The tunneling radiation of particles from black holes in Lovelock-Born-Infeld (LBI) gravity is studied by using the Parikh-Wilczek (PW) method, and the emission rate of a particle is calculated. It is shown that the emission spectrum deviates from the purely thermal spectrum but is consistent with an underlying unitary theory. Compared to the conventional tunneling rate related to the increment of black hole entropy, the entropy of the black hole in LBI gravity is obtained. The entropy does not obey the area law unless all the Lovelock coefficients equal zero, but it satisfies the first law of thermodynamics and is in accordance with earlier results. It is distinctly shown that the PW tunneling framework is related to the thermodynamic laws of the black hole.

The third order correction on Hawking radiation and entropy conservation during black hole evaporation process

Abstract Using Parikh–Wilczek tunneling framework, we calculate the tunneling rate from a Schwarzschild black hole under the third order WKB approximation, and then obtain the expressions for emission spectrum and black hole entropy to the third order correction. The entropy contains four terms including the Bekenstein–Hawking entropy, the logarithmic term, the inverse area term, and the square of inverse area term. In addition, we analyse the correlation between sequential emissions under this approximation. It is shown that the entropy is conserved during the process of black hole evaporation, which consists with the request of quantum mechanics and implies the information is conserved during this process. We also compare the above result with that of pure thermal spectrum case, and find that the non-thermal correction played an important role.

The Concrete Quantum Tunneling Spectrum of Reissner-Nordstrom Black Holes

A canonical ensemble model for a R-N black hole quantum tunneling radiation is introduced in this paper. We discover that the probability distribution function is equal to the emission rate of a spherical shell in the Parikh-Wilczek tunneling framework. Taking the generalized uncertainty principle into account, the probability distribution function corresponding to the emission shell system can be calculated with this model. As a result the concrete quantum tunneling spectrum for a R-N black hole is obtained.

Concrete quantum tunneling spectrum of Schwarzschild black holes**Project supported by the National Natural Science Foundation of China (Grant Nos. 11273009 and 11303006).

In this paper, a canonical ensemble model for black hole quantum tunneling radiation is introduced. We find that the probability distribution function is the same as the emission rate of a spherical shell in the Parikh–Wilczek tunneling framework. With this model, the probability distribution function corresponding to the emission shell system is calculated. Therefore, the concrete quantum tunneling spectrum of the Schwarzschild black hole is obtained.

Discussion on event horizon and quantum ergosphere of dynamic rotating black holes in a tunneling framework

According to the Parikh—Wilczek tunneling framework, the locations of the local horizons of dynamic rotating black holes can be worked out. The calculations show that the quantum ergosphere of the black hole is identical with the tunneling potential barrier set by particle's tunneling across the relevant horizon. Then, some discussions on the origin of the Hawking radiation will be shown.

Black Hole Entropy Calculation in a Modified Thin Film Model

The thin film model is modified to calculate the black hole entropy. The difference from the original method is that the Parikh–Wilczek tunnelling framework is introduced and the self-gravitation of the emission particles is taken into account. In terms of our improvement, if the entropy is still proportional to the area, then the emission energy of the particles will satisfy ω = T/360.

Discussion on event horizon and quantum ergosphere of evaporating black holes in a tunnelling framework

In this paper, with the Parikh-Wilczek tunnelling framework the positions of the event horizon of the Vaidya black hole and the Vaidya-Bonner black hole are calculated respectively. We find that the event horizon and the apparent horizon of these two black holes correspond respectively to the two turning points of the Hawking radiation tunnelling barrier. That is, the quantum ergosphere coincides with the tunnelling barrier. Our calculation also implies that the Hawking radiation comes from the apparent horizon.

Entropy correction of BTZ black holes in a tunneling framework

In this paper, using the Parikh-Wilczek tunneling framework, we first calculate the emission rates of non-rotating BTZ black holes and rotating BTZ black holes to second order accuracy. Then, by assuming that the emission process satisfies an underlying unitary theory, we obtain the corrected entropy of the BTZ black holes. A log term emerges naturally in the expression of the corrected entropy. A discussion about the inverse area term is also presented.

Tunneling Radiation from a Static Spherically Symmetric Black Hole Surrounded by Quintessence

By extending the Parikh–Wilczek tunneling framework, we investigate the tunneling radiation of uncharged massless particles from a static spherically symmetric black hole surrounded by quintessence. The results are consistent with an underlying unitary theory.

Black hole entropy, log correction and inverse area correction

In this Letter, we first extend the Parikh–Wilczek tunneling framework to a general spherically symmetric black hole, and calculate the tunneling rate of the emission particles to the second order accuracy. Then, by assuming the emission process satisfies an underlying unitary theory, we correct the entropy of a general spherically symmetric black hole. We find that the log correction and the inverse area correction to the entropy is also suitable for a general spherically symmetric black hole.

Black hole quantum tunnelling and black hole entropy correction

The Parikh–Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is investigated once more in this work. The first order correction, the log-corrected entropy-area relation, emerges naturally in the tunnelling picture if we consider the emission of a spherical shell. The second order correction to the emission rate for the Schwarzschild black hole is also calculated. At this level, the entropy of the black hole will contain three parts: the usual Bekenstein–Hawking entropy, a logarithmic term and an inverse area term. We find that the coefficient of the logarithmic term is −1. Thus, apart from a coefficient, our correction to the black hole entropy is consistent with that calculated in loop quantum gravity.

Tunnelling Radiation of Charged and Magnetized Massive Particles from BTZ Black Holes

We investigate the tunnelling radiation of charged and magnetized massive particles from a Bañados–Teitelboim–Zanelli (BTZ) black hole by extending the Parikh–Wilczek tunnelling framework. In order to calculate the emission rate, we reconstruct the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges, and treat the charges as an equivalent electric charge for simplicity in the later calculation. The result supports Parikh–Wilczek's conclusion, that is, the Hawking thermal radiation actually deviates from perfect thermality and agrees with an underlying unitary theory.

TUNNELING EFFECT OF CHARGED AND MAGNETIZED PARTICLES FROM THE REISSNER–NORDSTRÖM BLACK HOLE WITH MAGNETIC CHARGES

In this paper, we first rewrite the Lagrangian density of the electromagnetic field corresponding to the source with electric and magnetic charges. Then, in the background of Reissner–Nordström black hole spacetime, we extend the Parikh–Wilczek tunneling framework and calculate the emission spectrum of the outgoing particles with electric and magnetic charges. For the sake of simplicity, we only consider the case that the rate of electric and magnetic charge of the emission particle is constant and equals that of the black hole. In this case, the emission spectrum deviates from the pure thermal spectrum, but it is consistent with an underlying unitary theory and takes the same functional form as that of the uncharged massless particles. Finally, a discussion about the result is presented.

Tunnelling effect of charged and magnetized particles from the Kerr–Newman–Kasuya black hole

Abstract In this Letter, we extend the Parikh–Wilczek tunnelling framework to calculate the emission rate of a particle with electric and magnetic charges. We first reconstruct the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges. Then, in the background of Kerr–Newman–Kasuya black hole spacetime, we calculate the emission spectrum of the outgoing particles with electric and magnetic charges. For the sake of simplicity, we only consider the case that the rate of electric and magnetic charge of the emission particle is constant and equals that of the black hole. In this case, the emission spectrum deviates from the pure thermal spectrum, but it is consistent with an underlying unitary theory and takes the same functional form as that of uncharged massless particles. Finally, discussions about the result are presented.

INFORMATION LOSS IN BLACK HOLE EVAPORATION

Parikh–Wilczek tunnelling framework is investigated again. We argue that Parikh–Wilczek's treatment, which satisfies the first law of black hole thermodynamics and consists with an underlying unitary theory, is only suitable for a reversible process. Due to the negative heat capacity, an evaporating black hole is a highly unstable system. That is, the factual emission process is irreversible, the unitary theory will not be satisfied and information loss is possible.

Charged particles' tunnelling from the Kerr–Newman black hole

In this letter, Parikh-Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is extended, and the emission rate of a charged particle tunnelling from the Kerr-Newman black hole is calculated. The emission spectrum takes the same functional form as that of uncharged particles and consists with an underlying unitary theory but deviates from the pure thermal spectrum. Moreover, our calculation indicates that the emission process is treated as a reversible process in the Parikh-Wilczek tunnelling framework, and the information conservation is a natural result of the first law of black hole thermodynamics.

Black hole entropy, log corrections and quantum ergosphere

Quantum gravity corrections to the probability of emission of a particle from a black hole in the Parikh–Wilczek tunneling framework are studied. We consider the effects of zero-point quantum fluctuations of the metric on the emission probability for a tunneling shell. Quantum properties of the geometry are responsible for the formation of a “quantum ergosphere” whose effects on the emission probability can be related to the emergence of a logarithmic correction to the Bekenstein–Hawking entropy–area formula.

TUNNELING THROUGH THE QUANTUM HORIZON

The emergence of quantum-gravity induced corrective terms for the probability of emission of a particle from a black hole in the Parikh–Wilczek tunneling framework is studied. It is shown, in particular, how corrections might arise from modifications of the surface gravity due to near horizon Planck-scale effects. Our derivation provides an example of the possible linking between Planck-scale departures from Lorentz invariance and the appearance of higher order quantum gravity corrections in the black-hole entropy-area relation.

Hawking radiation as tunneling through the quantum horizon

Planck-scale corrections to the black-hole radiation spectrum in the Parikh-Wilczek tunneling framework are calculated. The corrective terms arise from modifications in the expression of the surface gravity in terms of the mass-energy of the black hole-emitted particle system. The form of the new spectrum is discussed together with the possible consequences for the fate of black holes in the late stages of evaporation.