Generalized second law at linear order for actions that are functions of Lovelock densities

TL;DR

The paper addresses whether the black hole second law extends to gravity theories with actions that are functions of Lovelock densities, and demonstrates a locally increasing entropy for linearized perturbations to regular Killing horizons, along with a semiclassical generalized second law for minimally coupled matter.It introduces the Jacobson-Myers entropy for Lanczos-Lovelock gravity and a generalized entropy for f(Lovelock) gravity, proving a classical second law and a linearized generalized second law under specific assumptions, including a regular bifurcation surface.The proofs rely on a linearized Raychaudhuri-type equation and relative-entropy arguments for the semiclassical case, clarifying when Wald entropy fails to satisfy a local second law and why JM entropy provides the correct intrinsic-horizon entropy in the relevant theories.These results constrain viable higher-curvature gravity theories by ensuring thermodynamic consistency in the linear regime and guide future work toward nonlinear effects and graviton contributions.

Abstract

In this article we consider the second law of black holes (and other causal horizons) in theories where the gravitational action is an arbitrary function of the Lovelock densities. We show that there exists an entropy which increases locally, for linearized perturbations to regular Killing horizons. In addition to a classical increase theorem, we also prove a generalized second law for semiclassical, minimally-coupled matter fields.