Logarithmic corrections to the entropy of near-extremal black holes in Einstein-Gauss-Bonnet

Abstract: We compute the one-loop contribution to the semiclassical partition function of near-extremal, asymptotically AdS black holes in five-dimensional Einstein-Gauss-Bonnet gravity. In the absence of an exact analytic rotating solution at finite Gauss-Bonnet coupling $α$, we restrict to static, charged configurations and evaluate the contribution to $Z_{\text{1-loop}}$ arising from tensor, vector, and $U(1)$ gauge fluctuations. The analysis is based on the spectrum of a generalized Lichnerowicz operator governing linearized perturbations on the near-horizon geometry of the extremal solution, including its deformation by the coupling $α$. In the canonical ensemble, the low-temperature behavior of the one-loop partition function leads to logarithmic corrections to the entropy of the form $\log(T/T_0)$, where the scale $T_0$ depends on both the fluctuation sector and the Gauss-Bonnet coupling. These corrections are controlled by the structure of zero modes of the deformed operator and their splitting at small but finite temperature. Our explicit computation yields a universal low-temperature scaling $Z_{\text{1-loop}}\sim 5 \log T$, where the coefficient arises from the combined contributions of tensor, vector, and $U(1)$ gauge modes, reflecting the corresponding counting of zero modes in each sector.