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## Area - Angular momentum inequality for axisymmetric black holes

### Abstract

We prove the local inequality $A \geq 8\pi|J|$, where $A$ and $J$ are the area and angular momentum of any axially symmetric closed stable minimal surface in an axially symmetric maximal initial data. From this theorem it is proved that the inequality is satisfied for any surface on complete asymptotically flat maximal axisymmetric data. In particular it holds for marginal or event horizons of black holes.Comment: Minor changes in the presentation. To appear in Phys. Rev. Letter

Topics: General Relativity and Quantum Cosmology
Year: 2011
DOI identifier: 10.1103/PhysRevLett.107.051101
OAI identifier: oai:arXiv.org:1102.5215