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In a recent work we have proved a weaker version of the Penrose inequalitywith angular momentum, in axially symmetric space-times, for a compact andconnected minimal surface. In this previous work we use the monotonicity ofGeroch energy on 2-surfaces along the inverse mean curvature flow and we obtaina lower bound for the ADM mass in terms of the area, the angular momentun and aparticular measure of size of the minimal surface. In the present work, usingsimilar techniques and the same measure of size, we extend and improve theprevious result for a compact and connected outermost apparent horizon. Forthis case we use the monotonicity of Hawking energy, instead of Geroch energy,along the inverse mean curvature flow, and assume different conditions on theextrinsic curvature. This type of relations constitutes an important test toevaluate the cosmic censorship conjecture.

Comments on Penrose inequality with angular momentum for outermost apparent horizons