Axisymmetric evolution of Einstein equations and mass conservation
General Relativity and Quantum Cosmology
2010-12-02 v3
Abstract
For axisymmetric evolution of isolated systems, we prove that there exists a gauge such that the total mass can be written as a positive definite integral on the spacelike hypersurfaces of the foliation and the integral is constant along the evolution. The conserved mass integral controls the square of the extrinsic curvature and the square of first derivatives of the intrinsic metric. We also discuss applications of this result for the global existence problem in axial symmetry.
Keywords
Cite
@article{arxiv.0804.2679,
title = {Axisymmetric evolution of Einstein equations and mass conservation},
author = {Sergio Dain},
journal= {arXiv preprint arXiv:0804.2679},
year = {2010}
}
Comments
A mistake in the proof of Lemma 5.1 is corrected. This version includes the Corrigendum that appears in Class. Quantum Grav. 26 (2009) 129801