A |torus like黑洞熵与能斯特定理

利用 Brick wall 方法,计算非球坐标系,非渐近平直的 torus like 黑洞背景下标量场的自由能和熵. 结果表明，在非渐近平直时空,黑洞具有内外视界时，所得熵不仅与外视界面积有关，而且也是内视界的函数.进一步证明，用内外视界参量表达的熵，在黑洞辐射温度趋于零时，黑洞的熵也趋于零，它满足能斯特定理，可视为黑洞的普朗克绝对熵.

The Nernst Theorem and the Entropy of= the A Torus like Black Hole

Using brick wall method, the authors calculate the free energy and entropy of the scalar field on the background of non asympotic flat torus like black hole under the sphere coordinates. The results show that the entropy not only is related to the area of an outer horizon but also is the function of a inner horizon. Furthermore, the entropy expressed by inner and outer horizon will approach zero when the radiation temperature of the black hole approaches zero. It satisfies the Nernst theorem. It can be taken as Planck absolute entropy.