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Isoperimetric inequality for higher dimensional black holes

Daisuke Ida
(
- Tokyo Inst. Tech.
)
,
Ken-ichi Nakao
(
- Osaka City U.
)

Apr, 2002

7 pages

Published in:

Phys.Rev.D 66 (2002) 064026

e-Print:

gr-qc/0204082 [gr-qc]

DOI:

10.1103/PhysRevD.66.064026

Report number:

OCU-PHYS-188

View in:

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Abstract: (arXiv)

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

.

04.70.Bw
04.50.+h
black hole
Einstein equation
dimension: 5
horizon
boundary condition
numerical calculations

References(24)

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