On Gauss-Bonnet black hole entropy

TL;DR

The paper analyzes black hole entropy in Gauss-Bonnet and Lovelock gravity using the Noether-charge (Iyer-Wald) formalism, expressing entropy as a horizon integral $S = 2\pi \int_{\Sigma} \mathbf{Q}[t]$ and showing it naturally splits into a horizon-area term plus curvature-driven corrections $S = \frac{1}{4G} \int_{\Sigma} \sqrt{\tilde{h}}(1+2\alpha\tilde{R})$ for Gauss-Bonnet, with a general Lovelock extension $S = 2\pi \int_{\Sigma} \sum_{p} p\alpha_p \tilde{L}^{(p-1)}$. The results reproduce prior Euclidean and first-law calculations and reveal an additive ambiguity in the entropy, arising from a closed but non-exact $(n-2)$-form tied to horizon topology, which can shift the entropy by a constant $S_{min}$ without violating the first law. This ambiguity can resolve apparent negative entropies by choosing an appropriate zero of entropy for a given family of solutions, though it reflects a topological rather than physical pathology. Overall, the work clarifies the geometric origin of entropy corrections in higher-curvature theories and emphasizes the influence of horizon topology on black hole thermodynamics.

Abstract

We investigate the entropy of black holes in Gauss-Bonnet and Lovelock gravity using the Noether charge approach, in which the entropy is given as the integral of a suitable (n-2) form charge over the event horizon. We compare the results to those obtained in other approaches. We also comment on the appearance of negative entropies in some cases, and show that there is an additive ambiguity in the definition of the entropy which can be appropriately chosen to avoid this problem.