Gravitational Entropy of Static Spacetimes and Microscopic Density of States
Year: 2003
Type: preprint
Abstract: A general definition 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. In any static spacetime with a horizon and associated temperature $\\beta^{-1}$, this entropy satisfies the relation $S=(1/2)\\beta E$ where $E$ is the energy source for gravitational acceleration, obtained as an integral of $(T_{ab}-(1/2)Tg_{ab})u^au^b$. With this definition of $S$, the minimisation of Einstein-Hilbert action is equivalent to minimising the free energy $F$ with $\\beta F=\\beta U-S$ where $U$ is the integral of $T_{ab}u^au^b$. We discuss the conditions under which these results imply $S\\propto E^2$ and/or $S\\propto U^2$. This approach links with several other known results, especially the holographic views of spacetime.
Source: arXiv (Cornell University)
Author: Τ. Padmanabhan
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963230092