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Entropy 2011, 13(2), 502-517; doi:10.3390/e13020502
Article

Microcanonical Description of (Micro) Black Holes

1,*  and 2
1 INFN Sezione di Bologna, c/o Dipartimento di Fisica, UniversitĂ  di Bologna, via Irnerio 46, 40126 Bologna, Italy 2 Department of Physics and Astronomy, University of Alabama, Box 870324, Tuscaloosa, AL 35487, USA
* Author to whom correspondence should be addressed.
Received: 12 January 2011 / Revised: 27 January 2011 / Accepted: 8 February 2011 / Published: 14 February 2011
(This article belongs to the Special Issue Entropy in Quantum Gravity)
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Abstract

The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existenceis predicted in models with extra-spatial dimensions.
Keywords: black holes; Hawking effect; microcanonical ensemble; extra dimensions black holes; Hawking effect; microcanonical ensemble; extra dimensions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Casadio, R.; Harms, B. Microcanonical Description of (Micro) Black Holes. Entropy 2011, 13, 502-517.

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