Towards a second law for Lovelock theories

TL;DR

This paper proposes a new entropy functional for Lovelock theories of gravity, extending the second law of black hole mechanics to dynamical black holes with higher derivative corrections.

Contribution

It introduces a perturbative entropy function for Lovelock theories that satisfies a second law, generalizing the classical area theorem to higher derivative gravity.

Findings

The entropy functional is valid to all orders in the low energy effective field theory.

It satisfies a second law modulo a subtle boundary term.

The approach treats higher derivative terms as perturbations to Einstein-Hilbert gravity.

Abstract

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.