On the existence of the logarithmic correction term in black hole entropy-area relation

In a dielectric black hole background, photons will be radiated via Hawking evaporation mechanism. In this paper, we calculate the entanglement entropy associated with a static dielectric black hole by employing 't Hooft's brick-wall model. It is found that the lowest energy of radiated particles is coordinate dependent. The resulted entanglement entropy is composed of three parts: a parameter independent leading constant term [Formula: see text], a logarithmic correction term and some series terms. The convergency of the series terms is also discussed.

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GUP-corrected thermodynamics for all black objects and the existence of remnants

International Journal of Modern Physics A ◽

10.1142/s0217751x15501444 ◽

2015 ◽

Vol 30 (22) ◽

pp. 1550144 ◽

Cited By ~ 55

Author(s):

Mir Faizal ◽

Mohammed M. Khalil

Keyword(s):

Black Holes ◽

Black Hole ◽

Correction Term ◽

Generalized Uncertainty Principle ◽

Logarithmic Correction ◽

Logarithmic Term ◽

Black Rings ◽

Corrected Entropy ◽

Ads Black Holes ◽

Full Form

Based on the universality of the entropy-area relation of a black hole, and the fact that the generalized uncertainty principle (GUP) adds a logarithmic correction term to the entropy in accordance with most approaches to quantum gravity, we argue that the GUP-corrected entropy-area relation is universal for all black objects. This correction to the entropy produces corrections to the thermodynamics. We explicitly calculate these corrections for three types of black holes: Reissner–Nordström, Kerr and charged AdS black holes, in addition to spinning black rings. In all cases, we find that they produce a remnant. Even though the GUP-corrected entropy-area relation produces the logarithmic term in the series expansion, we need to use the full form of the GUP-corrected entropy-area relation to get remnants for these black holes.

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A Study on the logarithm correction of black hole entropy

Journal of Physics Conference Series ◽

10.1088/1742-6596/2083/2/022042 ◽

2021 ◽

Vol 2083 (2) ◽

pp. 022042

Author(s):

Chengyu Liu ◽

Minxing Wang ◽

Guanxing Yi ◽

Yi Zhuang

Keyword(s):

Field Theory ◽

Black Hole ◽

Conformal Field Theory ◽

General Expression ◽

Correction Term ◽

Black Hole Entropy ◽

Thermal Method ◽

Btz Black Hole ◽

Conformal Field ◽

Loop Gravity

Abstract The logarithm correction of black hole entropy is important in understanding the essence of black hole entropy, providing a more accurate entropy calculation. We reviewed the mainstream method of logarithm correction of black hole entropy, including quantum loop gravity correction, conformal field theory correction, and classical thermal correction. Specifically, the correction of quantum loop gravity presents a stable general expression of logarithm correction, which only depends on the surface area of the black hole and solves the problem of meaningless entropy solution under a large length scale. Besides, the correction of the Cardy formula of conformal field theory is limited for the third term in depends on the mass of the black hole, which will finally lead to the unstable coefficient before the correction term. Finally, the correction deduced by the classical thermal method also gives a general expression of black hole entropy. In contrast, the entropy of BTZ black hole has a different coefficient before the logarithm term comparing to other kinds of the black hole. These results shed light for the research in general logarithm correction of black hole entropy, which is suitable for all kinds of black holes.

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FROM QUBITS TO BLACK HOLES: ENTROPY, ENTANGLEMENT AND ALL THAT

International Journal of Modern Physics D ◽

10.1142/s0218271805007802 ◽

2005 ◽

Vol 14 (12) ◽

pp. 2307-2314 ◽

Cited By ~ 12

Author(s):

DANIEL R. TERNO

Keyword(s):

Black Holes ◽

Black Hole ◽

Loop Quantum Gravity ◽

Black Hole Entropy ◽

Logarithmic Correction ◽

Evaporation Process ◽

Spin Networks ◽

Black Hole Evaporation ◽

Single Qubit

Entropy plays a crucial role in the characterization of information and entanglement, but it is not a scalar quantity and for many systems it is different for different relativistic observers. We discuss two examples: entropy of a single qubit and renormalized entropy as given by a uniformly accelerated observer. Loop quantum gravity predicts the Bekenstein–Hawking term for black hole entropy and the logarithmic correction to it. The latter originates in the entanglement between the pieces of spin networks that describe black hole horizon. Entanglement between gravity and matter may restore the unitarity in the black hole evaporation process. If the collapsing matter is assumed to be initially in a pure state, then entropy of the Hawking radiation is exactly the created entanglement between matter and gravity.

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Logarithmic correction of the BTZ black hole and adaptive model of graphene

International Journal of Modern Physics D ◽

10.1142/s0218271818501183 ◽

2018 ◽

Vol 27 (12) ◽

pp. 1850118 ◽

Cited By ~ 8

Author(s):

Behnam Pourhassan ◽

Mir Faizal ◽

S. Ahmad Ketabi

Keyword(s):

Black Holes ◽

Black Hole ◽

Quantum Gravity ◽

Correction Term ◽

Thermal Fluctuations ◽

Logarithmic Correction ◽

Adaptive Model ◽

Btz Black Hole ◽

The Real ◽

Almost All

It is known that almost all approaches to quantum gravity produce a logarithmic correction term to the entropy of a black hole, but the exact coefficient of such a term varies between the different approach to quantum gravity. Such logarithmic terms can also occur due to thermal fluctuations in both analogous and real black holes so that we will analyze the effects of logarithmic corrections term with variable coefficient on properties of analogous black hole. As these properties can be experimentally tested, they can be used to obtain the correct coefficient for such terms for an analogous black hole. We will argue that as even the real black holes can be considered as thermodynamical objects in Jacobson formalism, so such analogous black holes can be used to obtain the correct coefficient for the real black holes, and this in turn can be used to select the correct approach to quantum gravity. In that case, we use an adaptive model of graphene, which is still far from real graphene, to investigate some thermodynamics quantities of BTZ black hole.

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ON HAWKING RADIATION AS TUNNELING WITH LOGARITHMIC CORRECTIONS

Modern Physics Letters A ◽

10.1142/s0217732305018025 ◽

2005 ◽

Vol 20 (23) ◽

pp. 1723-1728 ◽

Cited By ~ 108

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.

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Thermal duality and thermodynamics of micro black holes

International Journal of Modern Physics D ◽

10.1142/s021827181550087x ◽

2015 ◽

Vol 24 (11) ◽

pp. 1550087 ◽

Cited By ~ 1

Author(s):

D. Jou ◽

M. Sciacca ◽

M. S. Mongiovì

Keyword(s):

Black Holes ◽

Black Hole ◽

Equation Of State ◽

Electromagnetic Radiation ◽

Cosmic String ◽

Correction Term ◽

Black Hole Entropy ◽

Generalized Equation ◽

The Other

Starting from a generalized black hole entropy with logarithmic area corrections, in this paper we obtain (for positive value of the coefficient of the correction term) a generalized equation of state for black holes with two dual branches. In one of them (the usual one for macro black holes) T ≃ 1/M, with T temperature and M mass. In the other one, for micro black holes, instead, T ≃ M. We compare the equilibrium and stability between macro black holes and electromagnetic radiation in a finite box with reflecting walls, with the dual situation corresponding to micro black holes and cosmic string loops, also in a finite box. In this model, the dual phenomenon of evaporation of unstable macro black holes into a stable gas of electromagnetic radiation would be the condensation of unstable gas of cosmic string loops into stable micro black holes.

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Logarithmic corrections to black hole entropy in matter coupled $$ \mathcal{N} $$ ≥ 1 Einstein-Maxwell supergravity

Journal of High Energy Physics ◽

10.1007/jhep05(2021)104 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Sudip Karan ◽

Binata Panda

Keyword(s):

Black Holes ◽

Black Hole ◽

Black Hole Entropy ◽

Logarithmic Correction ◽

Supergravity Theory ◽

Entropy Correction ◽

Logarithmic Corrections ◽

Entropy Corrections ◽

Massless Fields ◽

Extremal Black Holes

Abstract We calculate the first three Seeley-DeWitt coefficients for fluctuation of the massless fields of a $$ \mathcal{N} $$ N = 2 Einstein-Maxwell supergravity theory (EMSGT) distributed into different multiplets in d = 4 space-time dimensions. By utilizing the Seeley-DeWitt data in the quantum entropy function formalism, we then obtain the logarithmic correction contribution of individual multiplets to the entropy of extremal Kerr-Newman family of black holes. Our results allow us to find the logarithmic entropy corrections for the extremal black holes in a fully matter coupled $$ \mathcal{N} $$ N = 2, d = 4 EMSGT, in a particular class of $$ \mathcal{N} $$ N = 1, d = 4 EMSGT as consistent decomposition of $$ \mathcal{N} $$ N = 2 multiplets ($$ \mathcal{N} $$ N = 2 → $$ \mathcal{N} $$ N = 1) and in $$ \mathcal{N} $$ N ≥ 3, d = 4 EMSGTs by decomposing them into $$ \mathcal{N} $$ N = 2 multiplets ($$ \mathcal{N} $$ N ≥ 3 → $$ \mathcal{N} $$ N = 2). For completeness, we also obtain logarithmic entropy correction results for the non-extremal Kerr-Newman black holes in the matter coupled $$ \mathcal{N} $$ N ≥ 1, d = 4 EMSGTs by employing the same Seeley-DeWitt data into a different Euclidean gravity approach developed in [17].

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GENERAL LOGARITHMIC CORRECTIONS TO BEKENSTEIN–HAWKING ENTROPY

Modern Physics Letters A ◽

10.1142/s021773230702230x ◽

2007 ◽

Vol 22 (23) ◽

pp. 1737-1743 ◽

Cited By ~ 5

Author(s):

REN ZHAO ◽

HAI-XIA ZHAO ◽

SHUANG-QI HU

Keyword(s):

Black Hole ◽

Order Approximation ◽

Generalized Uncertainty Principle ◽

Black Hole Entropy ◽

Thermal Capacity ◽

Logarithmic Correction ◽

Logarithmic Term ◽

Entropy Correction ◽

The One ◽

First Order Approximation

Recently, there has been a lot of attention devoted to resolving the quantum corrections to the Bekenstein–Hawking entropy of the black hole. In particular, the coefficient of the logarithmic term in the black hole entropy correction has been of great interest. In this paper, the black hole is corresponded to a canonical ensemble in statistics by radiant spectrum, resulted from the black hole tunnelling effect studies and the partition function of ensemble is derived. Then the entropy of the black hole is calculated. When the first-order approximation is taken into account, the logarithmic term of entropy correction is consistent with the result of the generalized uncertainty principle. In our calculation, there are no uncertainty factors. The prefactor of the logarithmic correction and the one if fluctuation is considered are the same. Our result shows that if the thermal capacity is negative, there is no divergent term. We provide a general method for further discussion on quantum correction to Bekenstein–Hawking entropy. We also offer a theoretical basis for comparing string theory and loop quantum gravity and deciding which one is more reliable.

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