Black hole thermodynamics probes the equivalence principle

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.