Essay: The Holography of Gravity Encoded in a Relation Between Entropy, Horizon Area, and Action for Gravity
Abstract
I provide a general proof of the conjecture that one can attribute an entropy to the area of any horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature T = β^{1} and evaluating the exact partition function Z(β). For spherically symmetric spacetimes with a horizon at r = a, the partition function has the generic form Z ~ exp[S  β E], where S = (1/4)4π 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 De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic.
 Publication:

General Relativity and Gravitation
 Pub Date:
 December 2002
 DOI:
 10.1023/A:1021171015146
 arXiv:
 arXiv:grqc/0205090
 Bibcode:
 2002GReGr..34.2029P
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Theory
 EPrint:
 Second Prize Essay in the Gravity Research Foundation Essay Contest, 2002