Isoperimetric inequality for higher-dimensional black holes
Isoperimetric inequality for higher-dimensional black holes
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DOI：
10.1103/physrevd.66.064026
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发表时间：
2002-04
影响因子：
5
通讯作者：
D. Ida;K. Nakao
中科院分区：
文献类型：
--
作者：
D. Ida;K. Nakao
对五维爱因斯坦方程的初始数据集进行了检验。系统被设计成使得黑洞（$\simeq S^3$）或黑环（$\simeq S^2\times S^1$）可以被发现。我们发现视界的典型长度可以变得任意大，但是视界的特征闭二维子流形的面积在上面被典型质量标度所限制。我们猜想，n维空间中黑洞的等周不等式由Vn-2} lesssim GM$给出，其中Vn-2表示视界典型闭截面的体积，M是典型质量标度，而不是用环长C$表示的C1/（n-2）}，后者仅在n=3$时成立.
The initial data sets for the five-dimensional Einstein equation have been examined. The system is designed such that the black hole ($\simeq S^3$) or the black ring ($\simeq S^2\times S^1$) can be found. We have found that the typical length of the horizon can become arbitrarily large but the area of characteristic closed two-dimensional submanifold of the horizon is bounded above by the typical mass scale. We conjecture that the isoperimetric inequality for black holes in $n$-dimensional space is given by $V_{n-2} \lesssim GM$, where $V_{n-2}$ denotes the volume of typical closed $(n-2)$-section of the horizon and $M$ is typical mass scale, rather than $C\lesssim (GM)^{1/(n-2)}$ in terms of the hoop length $C$, which holds only when $n=3$.