NUMERICAL BLACK-HOLES - A MOVING GRID APPROACH

Spherically symmetric (one-dimensional) (black-hole) spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition, is presented. Significant errors in the mass function are shown to arise from the steep gradient zone behind the black-hole horizon, which challenge the computational fluid dynamics numerical methods used in the code. The formalism is extended to moving numerical grids, which are adapted to follow horizon motion. The black-hole exterior region can then be modeled with higher accuracy. © 1995 The American Physical Society.