2025/05/22 by C. Fairoos, Fairoos, C., Chiranjeeb Singha +1
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.2505.16309
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we derive the entropy of Reissner-Nordström (RN) and Kerr black holes using the Hawking-Gibbons path integral method. We determine the periodicity of the Euclidean time coordinate using two approaches: first, by analyzing the near-horizon geometry, and second, by applying the Chern-Gauss-Bonnet (CGB) theorem. For non-extremal cases, both these methods yield a consistent and unique periodicity, which in turn leads to a well-defined expression for the entropy. In contrast, the extremal case exhibits a crucial difference. The absence of a conical structure in the near-horizon geometry implies that the periodicity of the Euclidean time is no longer uniquely fixed within the Hawking-Gibbons framework. The CGB theorem also fails to constrain the periodicity, as the corresponding Euler characteristic vanishes. As a result, the entropy cannot be uniquely determined using either method.