2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200421We show that the Gauss-Bonnet term can have physical effects in four dimensions. Specifically, the entropy of a black hole acquires a correction that is proportional to the Euler characteristic of the cross sections of the horizon. While this term is constant for a single black hole, it will be a non-trivial function for a system with dynamical topologies such as black-hole mergers: it is shown that for certain values of the GB parameter, the second law of black-hole mechanics can be violated.8 pages; 1 figure; v2: 9 pages; some comments added at the end; 3 references added; v3: minor corrections; v4: some corrections; discussion added on black-hole mergers and violations of the second law; 2 references added; v5: minor corrections; v6: final corrections to match PRD versionGeneral Relativity and Quantum Cosmologytext