Path Integrals for Causal Diamonds and the Covariant Entropy Principle

TL;DR

This paper investigates causal diamonds across various spacetimes using Euclidean methods, revealing boundary contributions linked to the maximal entropy of gravitational degrees of freedom, supporting the covariant entropy principle.

Contribution

It demonstrates that boundary terms around causal diamonds correspond to their maximal gravitational entropy, providing a geometric and Euclidean perspective on holographic entropy bounds.

Findings

Boundary terms reduce Euclidean action by A/4

Null boundaries map to punctures in Euclidean space

Boundary contributions relate to maximal gravitational entropy

Abstract

We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_\diamond/4$, where $A_\diamond$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.