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Journal Article

Axisymmetric evolution of Einstein equations and mass conservation

MPS-Authors

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

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Fulltext (public)

cqg8_14_145021.pdf
(Publisher version), 229KB

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Citation

Dain, S. (2008). Axisymmetric evolution of Einstein equations and mass conservation. Classical and Quantum Gravity, 25(14): 145012. doi:10.1088/0264-9381/25/14/145021.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-635A-D
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.