Thermodynamics of Local Causal Horizons

TL;DR

This paper extends the thermodynamic interpretation of horizons to local causal horizons in any diffeomorphism invariant gravity theory, proposing an entropy density that satisfies the Clausius relation if the first law holds.

Contribution

It introduces a general expression for entropy density of local causal horizons that aligns with thermodynamic laws in various gravity theories.

Findings

Entropy density satisfies the Clausius relation under the first law

Thermodynamic properties of horizons are applicable beyond black holes

The approach is valid for any diffeomorphism invariant gravity theory

Abstract

We propose an expression for the entropy density associated with the Local Causal Horizons in any diffeomorphism invariant theory of gravity. If the black-hole entropy of the theory satisfies the physical process version of the first law of thermodynamics then our proposed entropy satisfies the Clausius relation. Thus, our study shows that the thermodynamic nature of the spacetime horizons is not restricted to the black holes; it also applies to the local causal horizons in the neighborhood of any point in the spacetime.