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The Penrose inequality and apparent horizons

Ishai Ben-Dov
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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 $M<\sqrt{A/16π}$, 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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Ishai Ben-Dov. 2005-01-05. The Penrose inequality and apparent horizons. https://doi.org/10.1103/physrevd.70.124031

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