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arXiv · hep-th/9701049

Collapsing Shells and the Isoperimetric Inequality for Black Holes

G W Gibbons
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Abstract

Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in Minkowski spacetime, the area $A$ of the apparent horizon is shown to be bounded above in terms of the mass $M$ by the $16 πG^2 M^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.

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G W Gibbons. 1997-01-13. Collapsing Shells and the Isoperimetric Inequality for Black Holes. https://doi.org/10.1088/0264-9381%2F14%2F10%2F016

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