Entropy-Area Relations in Field Theory

TL;DR

This paper investigates how entropy contributions from fields in curved spacetimes can be understood through a position-dependent UV cutoff, revealing insights into the dimensionality of gravitational systems.

Contribution

It introduces a position-dependent UV cutoff to account for curvature effects, providing a unified way to compute entropy in various curved backgrounds.

Findings

Entropy scales with local energy and volume in curved spacetimes

Results suggest an effective reduction in dimensionality due to gravity

Calculations performed for AdS, black hole, and de Sitter backgrounds

Abstract

We consider the contribution to the entropy from fields in the background of a curved time-independent metric. To account for the curvature of space, we postulate a position-dependent UV cutoff. We argue that a UV cutoff on energy naturally implies an IR cutoff on distance. With this procedure, we calculate the scalar contribution in a background anti-de Sitter space, the exterior of a black hole, and de Sitter space. In all cases, we find results that can be simply interpreted in terms of local energy and proper volume, yielding insight into the apparent reduced dimensionality of systems with gravity.