On the Universality of Inner Black Hole Mechanics and Higher Curvature Gravity

TL;DR

This paper investigates the universality of thermodynamic relations in black holes, especially the mass independence of entropy products, under higher curvature gravity corrections, revealing that this universality generally does not hold.

Contribution

It extends the study of black hole thermodynamics to higher curvature theories, showing that the mass independence of entropy products is not universally valid.

Findings

Mass independence of entropy product holds in some cases but generally fails with higher curvature corrections.

Derived thermodynamic relations for inner horizons in higher curvature gravity.

Identified relations between inner and outer horizon thermodynamic potentials.

Abstract

Black holes are famous for their universal behavior. New thermodynamic relations have been found recently for the product of gravitational entropies over all the horizons of a given stationary black hole. This product has been found to be independent of the mass for all such solutions of Einstein-Maxwell theory in d=4,5. We study the universality of this mass independence by introducing a number of possible higher curvature corrections to the gravitational action. We consider finite temperature black holes with both asymptotically flat and (A)dS boundary conditions. Although we find examples for which mass independence of the horizon entropy product continues to hold, we show that the universality of this property fails in general. We also derive further thermodynamic properties of inner horizons, such as the first law and Smarr relation, in the higher curvature theories under consideration, as well as a set of relations between thermodynamic potentials on the inner and outer horizons that follow from the horizon entropy product, whether or not it is mass independent.