Tolman mass, generalized surface gravity, and entropy bounds

TL;DR

This paper establishes a connection between Tolman mass, surface gravity, and entropy bounds in static spacetimes, deriving holographic-like entropy limits using thermodynamics and the Unruh effect.

Contribution

It introduces a novel relation between quasi-local mass, surface gravity, and entropy bounds, extending holographic principles in static spacetimes.

Findings

Derived surface integral expression for Tolman mass

Established entropy bounds analogous to holographic bounds

Linked entropy bounds to entanglement entropy via thermodynamics and Unruh effect

Abstract

In any static spacetime the quasi-local Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics and invoking the Unruh effect one can then develop elementary bounds on the quasi-local entropy that are very similar in spirit to the holographic bound, and closely related to entanglement entropy.