Starting from metric of the general non-extreme 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. D54, 3932(1996)) is extended to the general stationary black hole and the nonminimally coupled scalar field. We last shown by comparing the two results that the statistical-mechanical entropy and one-loop correction to the thermodynamical entropy are equivalent for coupling $\xi\leq 0$. After renormalization, a relation between the two entropies is given.
展开▼
机译:从四维时空中一般非极端静止轴对称黑洞的度量出发,研究了统计力学和热力学熵。首先,借助“砖墙”模型,其中Dirichlet条件被用于水平场场函数的散射ansatz代替,并利用Pauli-Villars正则化方案,表达了由非最小耦合产生的统计力学熵的表达式。获得标量字段。然后,通过使用圆锥奇异方法,Mann和Solodukhin对Kerr-Newman黑洞的结果(Phys。Rev. D54,3932(1996))扩展到一般的静态黑洞和非最小耦合标量场。通过比较两个结果,我们最后表明,统计力学熵和热力学熵的单环校正等效于耦合$ \ xi \ leq 0 $。重新归一化之后,给出两个熵之间的关系。
展开▼