A variational principle for stationary, axisymmetric solutions of Einstein's equations

Details A variational principle for stationary, axisymmetric solutions of Einstein's equations A variational principle for stationary, axisymmetric solutions of Einstein's equations

2005-08-16

arxiv.org/abs/gr-qc/0508061v1

Class.Quant.Grav. 23 (2006) 6857-6872

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages

Scientific paper

10.1088/0264-9381/23/23/016

Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.

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