On the Penrose Inequality for General Horizons

Edward Malec, Marc Mars, and Walter Simon
Phys. Rev. Lett. 88, 121102 – Published 6 March 2002
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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.

  • Received 21 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.121102

©2002 American Physical Society

Authors & Affiliations

Edward Malec

  • Instytut Fizyki, Uniwersytet Jagielloński, Reymonta 4, P-30-059 Kraków, Poland

Marc Mars

  • Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14 476 Golm, Germany

Walter Simon

  • Institut für Theoretische Physik der Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

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Vol. 88, Iss. 12 — 25 March 2002

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