Isoperimetric inequality for higher-dimensional black holes

Details Isoperimetric inequality for higher-dimensional black holes Isoperimetric inequality for higher-dimensional black holes

2002-04-26

arxiv.org/abs/gr-qc/0204082v1

Phys.Rev. D66 (2002) 064026

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, 13 figures

Scientific paper

10.1103/PhysRevD.66.064026

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 $n=3$.

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