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Register a new userBrick wall and quantum statistical entropy of black hole
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Authors
Sergey Solodukhin
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We discuss the statistical-mechanical entropy of black hole calculated according to t Hooft. It is argued that in presence of horizon the statistical mechanics of quantum fields depends on their UV behavior. The ``brick wall model was shown to provide a correct description when the ``brick wall parameter is less than any UV cut-off.
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We calculate the statistical entropy of a quantum field with an arbitrary spin propagating on the spherical symmetric black hole background by using the brick wall formalism at higher orders in the WKB approximation. For general spins, we find that the correction to the standard Bekenstein-Hawking entropy depends logarithmically on the area of the horizon. Furthermore, we apply this analysis to the Schwarzschild and Schwarzschild-AdS black holes and discuss our results.
We revisit the brick wall model for black hole entropy taking into account back-reaction effects on the horizon structure. We do so by adopting an evaporating metric in the quasi-static approximation in which departures from the standard Schwarzschild metric are governed by a small luminosity factor. One of the effects of the back-reaction is to create an ergosphere-like region which naturally tames the usual divergence in the calculation of the partition function of the field. The black hole luminosity sets the width of such quantum ergosphere. We find a finite horizon contribution to the entropy which, for the luminosity associated to the Hawking flux, agrees remarkably well with the Bekenstein-Hawking relation.
We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to t Hooft and regularized by Pauli-Villars.
We give a brief overview of black hole entropy, covering a few main developments since Bekensteins original proposal
The statistical-mechanical origin of the Bekenstein-Hawking entropy $S^{BH}$ in the induced gravity is discussed. In the framework of the induced gravity models the Einstein action arises as the low energy limit of the effective action of quantum fields. The induced gravitational constant is determined by the masses of the heavy constituents. We established the explicit relation between statistical entropy of constituent fields and black hole entropy $S^{BH}$.
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