The Second Law in Four-Dimensional Einstein-Gauss-Bonnet Gravity

The topological contribution of a Gauss–Bonnet term in four dimensions to black hole entropy opens up the possibility of a violation of the second law of thermodynamics in black hole mergers. We show, however, that the second law is not violated in the regime where Einstein–Gauss–Bonnet holds as an effective theory and black holes can be treated thermodynamically. For mergers of anti-de Sitter (AdS) black holes, the second law appears to be violated even in Einstein gravity; we argue, however, that the second law holds when gravitational potential energy is taken into account.