Static black holes with a negative cosmological constant: Deformed horizon and anti–de Sitter boundaries
Static black holes with a negative cosmological constant: Deformed horizon and anti–de Sitter boundaries
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具有负宇宙学常数的静态黑洞：变形视界和反德西特边界
DOI：
10.1103/physrevd.69.124034
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发表时间：
2004
影响因子：
5
通讯作者：
A. Tomimatsu
中科院分区：
文献类型：
--
作者：
H. Yoshino;Tohru Ohba;A. Tomimatsu
利用微扰技术，我们研究了具有负宇宙学常数的爱因斯坦方程的静态解的存在性和性质，我们称之为变形黑洞。我们导出了Schwarzschild\char21{}anti-de Sitter黑洞的静态轴对称扰动的一个解，该扰动在从视界到类空无穷远的范围内是正则的。关键的结果是，这种扰动同时使两个边界面变形\char22 {}，在无穷远处的视界和类空两面。然后讨论了变形黑洞的Abbott-Deser质量和Ashtekar-Magnon质量，并根据Ashtekar-Magnon定义，构造了变形黑洞的热力学第一定律。第一定律有一个修正项，它可以解释为边界面变形所需的功项。由于功项为负，变形黑洞的视界面积变得大于Schwarzschild\char21{}anti-de Sitter黑洞的视界面积，如果在相同质量下比较，表明Schwarzschild\char21{}anti-de Sitter黑洞的准静态变形可能与热力学第二定律相容（即，面积定理）。
Using perturbative techniques, we investigate the existence and properties of a static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild\char21{}anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces\char22{}i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild\char21{}anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild\char21{}anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).