Collapsing Shells and the Isoperimetric Inequality for Black Holes

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 $16\pi G^2{M}^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.

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