Article

Logarithmic Correction to the Bekenstein-Hawking Entropy

The Institute of Mathematical Sciences, Chennai 600 113, India.
Physical Review Letters (Impact Factor: 7.51). 03/2000; 84(23). DOI: 10.1103/PhysRevLett.84.5255
Source: arXiv

ABSTRACT

The exact formula derived by us earlier for the entropy of a four dimensional non-rotating black hole within the quantum geometry formulation of the event horizon in terms of boundary states of a three dimensional Chern-Simons theory, is reexamined for large horizon areas. In addition to the {\it semiclassical} Bekenstein-Hawking contribution to the area obtained earlier, we find a contribution proportional to the logarithm of the area together with subleading corrections that constitute a series in inverse powers of the area.

Download full-text

Full-text

Available from: Parthasarathi Majumdar, Jan 12, 2013
  • Source
    • "or relate temperature, energy and the number of used degrees of freedom using equipartition rule(19)It is necessary to point that the temperature T in equations (18) and (19) have different meaning. In the first equation, the temperature is defined in the bulk. "
    [Show abstract] [Hide abstract]
    ABSTRACT: One proposal by Verlinde \cite{Verlinde:2010hp} is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that these corrections could be inherited by the Newton's law. In this way, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. Loop quantum gravity is a theory that provide a way to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black holes or self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain the quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes. In order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.
    Full-text · Article · Jan 2016
  • Source
    • "A direct computation revealed a logarithmic correction to the BH entropy. Finally, the logarithmic correction was also found based on the quantum geometry program [49]. Now we summarize our results. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
    Preview · Article · Nov 2015
  • Source
    • "Expressions of this kind have been derived also from different perspectives, in different theoretical frameworks, and with different values of b, according to the different theoretical models. For instance, in Loop Quantum Gravity [13], [14], expression (2.2) has been obtained from microscopic grounds, but with b = −3/2 [14], [15]; the coefficient b = −3/2 was subsequently shown to be universal in this framework [16], [17] while F is a positive constant, to be commented below. However, in the loop quantum gravity approach, the black hole entropy formula (together with the log corrections) is explicitly valid only for large macroscopic black holes. "
    [Show abstract] [Hide abstract]
    ABSTRACT: 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.
    Full-text · Article · Jul 2015 · International Journal of Modern Physics D
Show more