1999/07/31 by Jiliang Jing, Mu-Lin Yan
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1103/physrevd.61.044016
published as Phys.Rev. D61 (2000) 044016 · 18 pages, Latex, nofigue. Accepted by Phys. Rev. D
arxiv created 1999/10/05 · openalex publication_date 2000/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from the metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermodynamical entropies are studied. First, by means of the ``brick wall'' model in which the Dirichlet condition is replaced by a scattering ansatz for the field functions at the horizon and with Pauli-Villars regularization scheme, an expression for the statistical-mechanical entropy arising from the nonminimally coupled scalar fields is obtained. Then, by using the conical singularity method Mann and Solodukhin's result for the Kerr-Newman black hole [Phys. Rev. D 54, 3932 (1996)] is extended to the general stationary black hole and the nonminimally coupled scalar field. We last show, by comparing the two results, that the statistical-mechanical entropy and one-loop correction to the thermodynamical entropy are equivalent for coupling \ensuremathξ<~0. After renormalization, a relation between the two entropies is given.