arXiv 2603.249392026-03-26hep-thgr-qc

五维爱因斯坦-高斯-博内引力中近极值黑洞熵的对数修正

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

Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Universidad de Concepción（康塞普西翁大学）；UNESP-Universidade Estadual Paulista（圣保罗州立大学）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）

Alejandro Alvarado, Andres Anabalon, Mariano Chernicoff, Julio Oliva, Marcelo Oyarzo, Gabriel Ortega, Jorge Urbina

备注：: 26 pages, no figures

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AI总结：

研究五维爱因斯坦-高斯-博内引力中近极值AdS黑洞的一阶修正，通过分析广义利钦诺维奇算子谱计算熵修正，发现温度依赖的对数修正。

摘要：

我们计算了五维爱因斯坦-高斯-博内引力中近极值AdS黑洞半经典分区函数的一阶贡献。在缺乏有限高斯-博内耦合α下的精确旋转解时，我们限制于静态带电配置，并计算张量、矢量和U(1)规范波动对Z_{1-loop}的贡献。分析基于广义利钦诺维奇算子的谱，该算子支配线性扰动在极值解近视界几何上的扰动，包括其由耦合α变形。在canonical集合中，低温行为导致熵的对数修正，形式为log(T/T_0)，其中T_0依赖于波动领域和高斯-博内耦合。这些修正由变形算子零模结构及其在小但有限温度下的分裂控制。我们的显式计算得出一个通用低温缩放Z_{1-loop}~5 log T，其中系数来自张量、矢量和U(1)规范模式的联合贡献，反映每个领域中零模的相应计数。

英文摘要：

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.

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