On the Penrose inequality for general horizons.
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.
Malec
Edward
E
Instytut Fizyki, Uniwersytet Jagielloński, Reymonta 4, P-30-059 Kraków, Poland.
Mars
Marc
M
Simon
Walter
W