A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
摘要
We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial hypersurfaces t=const, which corresponds to the asymptotic structure of the physical 3-metric induced by the spacetime metric. Thanks to the joint use of Dirac gauge, maximal slicing and spherical components of tensor fields, the ten Einstein equations are reduced to a system of five quasi-linear elliptic equations (including the Hamiltonian and momentum constraints) coupled to two quasi-linear scalar wave equations. The remaining three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows a direct computation of the spherical components of the conformal metric from the two scalar potentials which obey the wave equations. We present some numerical evolution of 3-D gravitational wave spacetimes which demonstrates the stability of the proposed scheme.
引用
@article{arxiv.gr-qc/0307082,
title = {A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates},
author = {S. Bonazzola and E. Gourgoulhon and P. Grandclement and J. Novak},
journal= {arXiv preprint arXiv:gr-qc/0307082},
year = {2007}
}
备注
Difference w.r.t. v1: Major revision: improved presentation of the tensor wave equation and addition of the first results from a numerical implementation; w.r.t. v2: Minor changes: improved conclusion and figures; w.r.t. v3: Minors changes, 1 figure added; 25 pages, 13 figures, REVTeX, accepted for publication in Phys. Rev. D