Multigrid in general relativity. I. Schwarzschild spacetime
Abstract
The multigrid method has been used to numerically solve the stationary axisymmetric Einstein equations in vacuum. Results have been obtained for the case where the equations are specialized to the Schwarzschild metric, with emphasis on the effect of singularities. The analysis takes into account the horizon and Neumann boundary conditions. The results indicate that the full multigrid algorithm 1FMG is sufficient for solving the equations to a level of truncation error. The method has application to the study of selfgravitating tori rotating around rapidly rotating black holes.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 May 1988
 DOI:
 10.1088/02649381/5/5/008
 Bibcode:
 1988CQGra...5..713B
 Keywords:

 Computational Grids;
 Conformal Mapping;
 Relativity;
 Schwarzschild Metric;
 SpaceTime Functions;
 Black Holes (Astronomy);
 Einstein Equations;
 Gravitational Effects;
 Singularity (Mathematics);
 Astrophysics