Black hole thermodynamics probes the equivalence principle

TL;DR

This paper introduces a criterion to detect violations of the equivalence principle in black hole thermodynamics, revealing that Lanczos-Lovelock gravity violates it while some nonlocal entropy expressions do not.

Contribution

It provides a simple theoretical test for equivalence principle violations in black hole thermodynamics and shows that Lanczos-Lovelock gravity does not satisfy this principle.

Findings

Lanczos-Lovelock gravity violates the strong equivalence principle

Certain nonlocal black hole entropy expressions obey the equivalence principle

General relativity remains compatible with the equivalence principle

Abstract

The equivalence principle for test gravitational physics strongly constrains dynamics of spacetime, providing a powerful criterion for selecting candidate theories of gravity. However, checking its validity for a particular theory is often a very difficult task. We devise here a simple theoretical criterion for identifying equivalence principle violations in black hole thermodynamics. Employing this criterion, we prove that Lanczos-Lovelock gravity violates the strong equivalence principle, leaving general relativity as the only local, diffeomorphism-invariant theory compatible with it. However, we also show that certain nonlocal expressions for black hole entropy appear to obey the strong equivalence principle.