A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
| dc.creator | Bonazzola, S. | |
| dc.creator | Gourgoulhon, E. | |
| dc.creator | Grandclement, P. | |
| dc.creator | Novak, J. | |
| dc.date | 2003-07-17 | |
| dc.date | 2004-09-21 | |
| dc.date.accessioned | 2026-07-07T03:27:59Z | |
| dc.date.available | 2026-07-07T03:27:59Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0307082 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0307082 | |
| dc.identifier | Phys.Rev. D70 (2004) 104007 | |
| dc.identifier | doi:10.1103/PhysRevD.70.104007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/34653 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates | |
| dc.type | text |