On the Penrose Inequality for general horizons

Details On the Penrose Inequality for general horizons On the Penrose Inequality for general horizons

2002-01-08

arxiv.org/abs/gr-qc/0201024v2

Phys.Rev.Lett. 88 (2002) 121102

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.88.121102

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. 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. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.

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