The Penrose inequality and apparent horizons
Ishai Ben-Dov
Abstract
A spherically symmetric spacetime is presented with an initial data set that is asymptotically flat, satisfies the dominant energy condition, and such that on this initial data M<A/16π, where M is the total (ADM) mass and A is the area of the apparent horizon. This provides a counterexample to a commonly stated version of the Penrose inequality, though it does not contradict the ``true'' Penrose inequality.
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