Article

# Logarithmic correction to the Bekenstein-Hawking entropy

The Institute of Mathematical Sciences, Chennai 600 113, India.

Physical Review Letters (Impact Factor: 7.73). 03/2000; DOI: 10.1103/PhysRevLett.84.5255 Source: arXiv

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**ABSTRACT:**Several investigations show that in a very small length scale there exists corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket among the charges is calculated. We show that the Fourier modes of the bracket is exactly similar to Virasoro algebra. Then using Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for entropy; i.e. the Bekenstein-Hawking form, is not modified.European Physical Journal C 05/2014; 74(May):2867. · 5.25 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The quantum mechanical structure of Schwarzschild black hole is probed, in the mini super spacetime, by means of a non-singular minimal uncertainty Hartle-Hawking wave packet. The Compton width of the microstate probability distribution is translated into a thermal Hawking broadening of the mass spectrum. The statistical entropy is analytically calculated using the Fowler prescription. While the exact Bekenstein-Hawking entropy is recovered at the semi classical limit, the accompanying logarithmic tail gives rise to a Planck size minimal entropy black wave packet.01/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Considering the quantum description of equilibrium black holes, given by the quantum isolated horizon framework in loop quantum gravity, the effect of closed topology of the horizon is studied. Black hole entropy is now given by $S=A_{cl}/4\ell_p^2+4\pi\rho(A_{cl})$, where $\rho(A_{cl})$ is a complicated function of the classical area of the horizon$(A_{cl})$. The expression is valid for any finite positive value of the Barbero-Immirzi parameter. The expression for the equilibrium temperature appearing in the first law of black hole mechanics (generalized for isolated horizons in present day literature) gets modified as a consequence. Furthermore, two very interesting predictions are made : i) there is a possible upper bound on the amount of holographic information that can be stored on the horizon of a black hole ii) the mass of a black hole is bounded above (which is at par with recent astrophysical observations based on experimental data).02/2014;

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