Entropy and energy of a class of spacetimes with horizon: a general derivation
Abstract
Euclidean continuation of several Lorentzian spacetimes with horizons requires treating the Euclidean time coordinate to be periodic with some period $\beta$. Such spacetimes (Schwarzschild, deSitter,Rindler .....) allow a temperature $T=\beta^{1}$ to be associated with the horizon. I construct a canonical ensemble of a subclass of such spacetimes with a fixed value for $\beta$ and evaluate the partition function $Z(\beta)$. For spherically symmetric spacetimes with a horizon at r=a, the partition function has the generic form $Z\propto \exp[S\beta E]$, where $S= (1/4) 4\pi a^2$ and $E=(a/2)$. Both S and E are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the blackhole spacetimes and provides a simple and consistent interpretation of entropy and energy for deSitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. The implications are discussed.
 Publication:

arXiv eprints
 Pub Date:
 February 2002
 arXiv:
 arXiv:grqc/0202080
 Bibcode:
 2002gr.qc.....2080P
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 revtex4