The Penrose inequality and apparent horizons

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 $M<\sqrt{A/16\pi }$, 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.

24 pages, 6 figures, revised for publication; revised section 6, added footnote no. 16, typos corrected