Axisymmetric evolution of Einstein equations and mass conservation

S. DAIN

CLASSICAL AND QUANTUM GRAVITY

IOP

Año: 2008 vol. 25 p. 145021 - 145021

0264-9381

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.