Proof of the angular momentum-mass inequality for axisymmetric black holes

Dain, S.

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Proof of the angular momentum-mass inequality for axisymmetric black holes

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Dain, S.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Dain, S. (2008). Proof of the angular momentum-mass inequality for axisymmetric black holes. Journal of Differential Geometry, 79(1), 33-67.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-63BD-2

Abstract

We prove that an 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 spacetime.