Increase of Black Hole Entropy in Higher Curvature Gravity

TL;DR

The paper investigates whether black hole entropy increase theorems extend to higher-curvature gravity. It uses conformal transformations to relate higher-curvature actions to Einstein gravity with auxiliary scalars, deriving Zeroth and Second Laws for a broad class of theories, and provides a direct proof via an extended Raychaudhuri framework for Ricci-polynomial actions. The authors obtain explicit entropy functionals, notably S = (1/4G) ∫ sqrt{h} (1+P'(R)) or (1+2αR), and show nondecreasing entropy under appropriate energy and stability conditions, while acknowledging instabilities and the need for cosmic censorship. The work strengthens the thermodynamic interpretation of black holes in generalized gravity, clarifies constraints on viable effective actions, and points toward generalized second-law considerations and perturbative approaches for broader applicability.

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.