Increase of Black Hole Entropy in Higher Curvature Gravity

TL;DR

This paper demonstrates that black hole entropy increases in higher curvature gravity theories during quasi-stationary processes, extending classical thermodynamic laws to more complex gravitational models.

Contribution

It establishes the validity of the Zeroth and Second Laws of black hole thermodynamics in higher curvature theories, introducing a new method for entropy calculation.

Findings

Entropy never decreases during accretion of positive energy matter.

Stationary black holes satisfy the Zeroth Law in these theories.

The Second Law holds generally for dynamical processes.

Abstract

We examine the Zeroth Law and the Second Law of black hole thermodynamics within the context of effective gravitational actions including higher curvature interactions. We show that entropy can never decrease for quasi-stationary processes in which a black hole accretes positive energy matter, independent of the details of the gravitational action. Within a class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar, we use a conformally equivalent theory to establish that stationary black hole solutions with a Killing horizon satisfy the Zeroth Law, and that the Second Law holds in general for any dynamical process. We also introduce a new method for establishing the Second Law based on a generalization of the area theorem, which may prove useful for a wider class of Lagrangians. Finally, we show how one can infer the form of the black hole entropy, at least for the Ricci polynomial theories, by integrating the changes of mass and angular momentum in a quasistationary accretion process.