Entropy of Static Spacetimes and Microscopic Density of States

T. Padmanabhan

doi:10.1088/0264-9381/21/18/013

paper

Entropy of Static Spacetimes and Microscopic Density of States

arXiv:gr-qc/0308070 · doi:10.1088/0264-9381/21/18/013

Abstract

A general ansatz for gravitational entropy can be provided using the criterion that, any patch of area which acts as a horizon for a suitably defined accelerated observer, must have an entropy proportional to its area. After providing a brief justification for this ansatz, several consequences are derived: (i) In any static spacetime with a horizon and associated temperature $β^{- 1}$ , this entropy satisfies the relation $S = (1/2) β E$ where $E$ is the energy source for gravitational acceleration, obtained as an integral of $(T_{ab} - (1/2) T g_{ab}) u^{a} u^{b}$ . (ii) With this ansatz of $S$ , the minimization of Einstein-Hilbert action is equivalent to minimizing the free energy $F$ with $β F = β U - S$ where $U$ is the integral of $T_{ab} u^{a} u^{b}$ . We discuss the conditions under which these results imply $S \propto E^{2}$ and/or $S \propto U^{2}$ thereby generalizing the results known for black holes. This approach links with several other known results, especially the holographic views of spacetime.

Extensively revised with more details and clarifications; 12 pages; accepted for publication in Class.Quant.Grav

Entropy of Static Spacetimes and Microscopic Density of States

Abstract

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