Entropy of thin shells in a (2+1)dimensional asymptotically AdS spacetime and the BTZ black hole limit
Abstract
The thermodynamic equilibrium states of a static thin ring shell in a (2+1)dimensional spacetime with a negative cosmological constant are analyzed. Inside the ring, the spacetime is pure antide Sitter, whereas outside it is a BañadosTeitelbomZanelli spacetime and thus asymptotically antide Sitter. The first law of thermodynamics applied to the thin shell, plus one equation of state for the shell's pressure and another for its temperature, leads to a shell's entropy, which is a function of its gravitational radius alone. A simple example for this gravitational entropy, namely, a power law in the gravitational radius, is given. The equations of thermodynamic stability are analyzed, resulting in certain allowed regions for the parameters entering the problem. When the Hawking temperature is set on the shell and the shell is pushed up to its own gravitational radius, there is a finite quantum backreaction that does not destroy the shell. One then finds that the entropy of the shell at the shell's gravitational radius is given by the BekensteinHawking entropy.
 Publication:

Physical Review D
 Pub Date:
 April 2014
 DOI:
 10.1103/PhysRevD.89.084051
 arXiv:
 arXiv:1403.0579
 Bibcode:
 2014PhRvD..89h4051L
 Keywords:

 04.40.b;
 04.70.Dy;
 Selfgravitating systems;
 continuous media and classical fields in curved spacetime;
 Quantum aspects of black holes evaporation thermodynamics;
 General Relativity and Quantum Cosmology
 EPrint:
 9 pages