Abstract
We prove the local inequality , where and 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. Hence, we prove the validity of this inequality for all dynamical (not necessarily near equilibrium) axially symmetric black holes.
- Received 10 March 2011
DOI:https://doi.org/10.1103/PhysRevLett.107.051101
© 2011 American Physical Society