Thermal relativity, modified Hawking radiation, and the generalized uncertainty principle

2019 ◽  
Vol 16 (10) ◽  
pp. 1950156
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Black Hole Entropy ◽  
The Novel ◽  
Black Hole Information ◽  
The One ◽  
Mini Black Holes

After a brief review of the thermal relativistic corrections to the Schwarzschild black hole entropy, it is shown how the Stefan–Boltzman law furnishes large modifications to the evaporation times of Planck-size mini-black holes, and which might furnish important clues to the nature of dark matter and dark energy since one of the novel consequences of thermal relativity is that black holes do not completely evaporate but leave a Planck size remnant. Equating the expression for the modified entropy (due to thermal relativity corrections) with Wald’s entropy should, in principle, determine the functional form of the modified gravitational Lagrangian [Formula: see text]. We proceed to derive the generalized uncertainty relation which corresponds to the effective temperature [Formula: see text] associated with thermal relativity and given in terms of the Hawking ([Formula: see text]) and Planck ([Formula: see text]) temperature, respectively. Such modified uncertainty relation agrees with the one provided by string theory up to first order in the expansion in powers of [Formula: see text]. Both lead to a minimal length (Planck size) uncertainty. Finally, an explicit analytical expression is found for the modifications to the purely thermal spectrum of Hawking radiation which could cast some light into the resolution of the black hole information paradox.

scholarly journals Islands and Page curves of Reissner-Nordström black holes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Xuanhua Wang ◽  
Ran Li ◽  
Jin Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Additional Term ◽  
Current Case ◽  
Information Paradox ◽  
Extremal Surface ◽  
Four Dimensions ◽  
Black Hole Information

Abstract We apply the recently proposed quantum extremal surface construction to calculate the Page curve of the eternal Reissner-Nordström black holes in four dimensions ignoring the backreaction and the greybody factor. Without the island, the entropy of Hawking radiation grows linearly with time, which results in the information paradox for the eternal black holes. By extremizing the generalized entropy that allows the contributions from the island, we find that the island extends to the outside the horizon of the Reissner-Nordström black hole. When taking the effect of the islands into account, it is shown that the entanglement entropy of Hawking radiation at late times for a given region far from the black hole horizon reproduces the Bekenstein-Hawking entropy of the Reissner-Nordström black hole with an additional term representing the effect of the matter fields. The result is consistent with the finiteness of the entanglement entropy for the radiation from an eternal black hole. This facilitates to address the black hole information paradox issue in the current case under the above-mentioned approximations.

Hawking radiation of charged fermions from accelerating and rotating black holes with generalized uncertainty principle

2019 ◽  
Vol 28 (08) ◽  
pp. 1950102
Author(s):  
Muhammad Rizwan ◽  
Khalil Ur Rehman
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Black Hole Evaporation ◽  
Rotating Black Holes ◽  
Gravity Effects ◽  
Made In

By considering the quantum gravity effects based on generalized uncertainty principle, we give a correction to Hawking radiation of charged fermions from accelerating and rotating black holes. Using Hamilton–Jacobi approach, we calculate the corrected tunneling probability and the Hawking temperature. The quantum corrected Hawking temperature depends on the black hole parameters as well as quantum number of emitted particles. It is also seen that a remnant is formed during the black hole evaporation. In addition, the corrected temperature is independent of an angle [Formula: see text] which contradicts the claim made in the literature.

The entropy evolution of a Schwarzschild–(Anti) de Sitter black hole

2020 ◽  
Vol 29 (07) ◽  
pp. 2050048
Author(s):  
Xin-Yang Wang ◽  
Yi-Ru Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Dynamical Variable ◽  
De Sitter ◽  
The One ◽  
Definition Of ◽  
Spherically Symmetry ◽  
Interior Volume

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ([Formula: see text]) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing [Formula: see text]. Furthermore, considering [Formula: see text] as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and [Formula: see text] under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and [Formula: see text] are both considered as dynamical variables.

Black-hole Information Loss Problem: Past, Present, and Future

2020 ◽  
Vol 29 (11) ◽  
pp. 17-25
Author(s):  
Sang-Heon YI ◽  
Dong-han YEOM
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Hawking Radiation ◽  
Recent Progress ◽  
Information Loss ◽  
Future Perspectives ◽  
Black Hole Information ◽  
Information Loss Problem

In this article, we discuss the information loss problem of black holes and critically review candidate resolutions of the problem. As a black hole evaporates via Hawking radiation, it seems to lose original quantum information; this indicates that the unitarity of time evolution in quantum mechanics and the fundamental predictability of physics are lost. We categorized candidate resolutions by asking (1) where information is and (2) which principle of physics is changed. We also briefly comment on the recent progress in the string theory community. Finally, we present several remarks for future perspectives.

scholarly journals Hawking radiation from z = 3 and z = 1-Lifshitz black holes

2014 ◽  
Vol 29 (34) ◽  
pp. 1450187
Author(s):  
Samuel Lepe ◽  
Bruno Merello
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Black Hole Entropy ◽  
Tunneling Rate ◽  
Btz Black Hole ◽  
Tunneling Process ◽  
Lifshitz Black Holes ◽  
Lifshitz Black Hole

The Hawking radiation considered as a tunneling process, by using a Hamilton–Jacobi prescription, is discussed for both z = 3 and z = 1-Lifshitz black holes. We have found that the tunneling rate (which is not thermal but related to the change of entropy) for the z = 3-Lifshitz black hole (which does not satisfy the Area/4-law) does not yield (give us) the expected tunneling rate: Γ~ exp (ΔS), where ΔS is the change of black hole entropy, if we compare with the z = 1-Lifshitz black hole (BTZ black hole, which satisfies the Area/4-law).

scholarly journals ON HAWKING RADIATION AS TUNNELING WITH LOGARITHMIC CORRECTIONS

2005 ◽  
Vol 20 (23) ◽  
pp. 1723-1728 ◽  
Author(s):  
A. J. M. MEDVED ◽  
ELIAS C. VAGENAS
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Black Hole Entropy ◽  
Gravitational Effect ◽  
Logarithmic Correction ◽  
Logarithmic Order ◽  
Logarithmic Term ◽  
Information Loss Paradox ◽  
Black Hole Information ◽  
Quantum Formulation

There has been recent speculation that the tunneling paradigm for Hawking radiation could — after quantum-gravitational effects have suitably been incorporated — provide a means for resolving the (black hole) information loss paradox. A prospective quantum-gravitational effect is the logarithmic-order correction to the Bekenstein–Hawking entropy/area law. In this paper, it is demonstrated that, even with the inclusion of the logarithmic correction (or, indeed, the quantum correction up to any perturbative order), the tunneling formalism is still unable to resolve the stated paradox. Moreover, we go on to show that the tunneling framework effectively constrains the coefficient of this logarithmic term to be non-negative. Significantly, the latter observation implies the necessity for including the canonical corrections in the quantum formulation of the black hole entropy.

scholarly journals Minimal length and the flow of entropy from black holes

2018 ◽  
Vol 27 (14) ◽  
pp. 1847028 ◽  
Author(s):  
Ana Alonso-Serrano ◽  
Mariusz P. Da̧browski ◽  
Hussain Gohar
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Evaporation Process ◽  
Black Hole Evaporation ◽  
The Impact

The existence of a minimal length, predicted by different theories of quantum gravity, can be phenomenologically described in terms of a generalized uncertainty principle. We consider the impact of this quantum gravity motivated effect onto the information budget of a black hole and the sparsity of Hawking radiation during the black hole evaporation process. We show that the information is not transmitted at the same rate during the final stages of the evaporation, and that the Hawking radiation is not sparse anymore when the black hole approaches the Planck mass.

scholarly journals CURVATURE, PHASE SPACE, HOLOGRAPHY AND BLACK HOLE ENTROPY

2009 ◽  
Vol 18 (14) ◽  
pp. 2167-2171 ◽  
Author(s):  
C. SIVARAM ◽  
KENATH ARUN
Keyword(s):  
Black Hole ◽  
Phase Space ◽  
Surface Area ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Black Hole Entropy ◽  
Black Hole Masses ◽  
Interior Volume

This paper discusses the thermodynamics of a black hole with respect to Hawking radiation and the entropy. We look at a unified picture of black hole entropy and curvature and how this can lead to the usual black hole luminosity due to Hawking radiation. It is also shown how the volume inside the horizon, apart from the surface area (hologram!), can play a role in understanding the Hawking flux. In addition, holography implies a phase space associated with the interior volume and this happens to be just a quantum of phase space, filled with just one photon. The generalized uncertainty principle can be incorporated in this analysis. These results hold for all black hole masses in any dimension.

scholarly journals THERMODYNAMIC GEOMETRY AND CRITICAL BEHAVIOR OF BLACK HOLES

2007 ◽  
Vol 22 (01) ◽  
pp. 11-27 ◽  
Author(s):  
JIANYONG SHEN ◽  
RONG-GEN CAI ◽  
BIN WANG ◽  
RU-KENG SU
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Critical Behavior ◽  
Hessian Matrix ◽  
Black Hole Entropy ◽  
De Sitter ◽  
Ads Black Holes ◽  
Gas System ◽  
The One

Based on the observations that there exists an analogy between the Reissner–Nordström–Anti-de Sitter (RN–AdS) black holes and the van der Waals–Maxwell liquid-gas system, in which a correspondence of variables is (ϕ,q) ↔ (V,P), we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN–AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN–AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.

scholarly journals Hawking radiation and the quantum marginal problem

2022 ◽  
Vol 2022 (01) ◽  
pp. 014
Author(s):  
Erik Aurell ◽  
Michał Eckstein ◽  
Paweł Horodecki
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Single Mode ◽  
New Physics ◽  
Continuous Variable ◽  
Marginal Problem ◽  
Recent Developments ◽  
Black Hole Information ◽  
Multi Mode

Abstract In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the “black hole information paradox”. Two main types of resolution postulate either a fundamental loss of information in Nature — hence the breakdown of quantum mechanics — or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we employ the solution to the Gaussian quantum marginal problem to show that the thermality of all individual Hawking modes is consistent with a global pure state of the radiation. Surprisingly, we find out that the mods of radiation of an astrophysical black hole are thermal until the very last burst. In contrast, the single-mode thermality of Hawking radiation originating from microscopic black holes, expected to evaporate through several quanta, is not excluded, though there are constraints on modes' frequencies. Our result paves the way towards a systematic study of multi-mode correlations in Hawking radiation.

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