Second Law Violations in Lovelock Gravity for Black Hole Mergers

TL;DR

This work examines the validity of the classical second law for black holes in Lovelock gravity beyond General Relativity. By analyzing the Wald entropy and its ambiguities, and through dimensional reduction of higher-dimensional Gauss-Bonnet theory, it demonstrates scenarios where the proposed entropy can decrease during black hole mergers, challenging the universality of the second law in Lovelock theories. The authors discuss potential resolutions, including new entropy definitions or quantum corrections, and highlight fundamental questions about horizon thermodynamics in non-GR gravity. The findings suggest that horizon entropy in Lovelock gravity may require modifications beyond the standard Wald construction to preserve a second-law-like behavior.

Abstract

We study the classical second law of black hole thermodynamics, for Lovelock theories (other than General Relativity), in arbitrary dimensions. Using the standard formula for black hole entropy, we construct scenarios involving the merger of two black holes in which the entropy instantaneously decreases. Our construction involves a Kaluza-Klein compactification down to a dimension in which one of the Lovelock terms is topological. We discuss some open issues in the definition of the second law which might be used to compensate this entropy decrease.

Figures (1)

• Figure 1: The head-on collision of two black holes, pictured on time slices before, at, and after the moment of joinder. While the horizons may be smooth after the collision, before the collision each of the two black holes must have a nonsmooth point.