PMID: 11909440Mar 23, 2002Paper

On the Penrose inequality for general horizons

Physical Review Letters
Edward MalecWalter Simon

Abstract

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an outermost apparent horizon, if the data are suitably restricted. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Leaving smoothness issues aside, we also show that our restrictions on the data can be locally fulfilled by a suitable choice of the initial surface in a given spacetime.

References

Jun 15, 1994·Physical Review. D·S A Hayward
Jun 15, 1994·Physical Review. D·E Malec, Ó Murchadha N
Sep 25, 2001·Physical Review Letters·J Frauendiener

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Citations

Jan 8, 2019·Living Reviews in Relativity·Sergio Dain, María Eugenia Gabach-Clement
Jan 1, 2004·Living Reviews in Relativity·László B Szabados
Jan 1, 2009·Living Reviews in Relativity·László B Szabados

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