Proof of the angular momentum-mass inequality for axisymmetric black holes
Sergio Dain
Abstract
We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence, we obtain that any data in this class satisfy the inequality J ≤ m, where m and J are the total mass and angular momentum of the spacetime.
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