Notes on causal differencing in ADM/CADM formulations: a 1D comparison
Abstract
Causal differencing has shown to be one of the promising and successful approaches towards excising curvature singularities from numerical simulations of black hole spacetimes. So far it has only been actively implemented in the ADM and Einstein-Bianchi 3+1 formulations of the Einstein equations. Recently, an approach closely related to the ADM one, commonly referred to as as ``conformal ADM'' (CADM) has shown excellent results when modeling waves on flat spacetimes and black hole spacetimes where singularity avoiding slices are used to deal with the singularity. In these cases, the use of CADM has yielded longer evolutions and better outer boundary dependence than those obtained with the ADM one. If this success translates to the case where excision is implemented, then the CADM formulation will likely be a prime candidate for modeling generic black hole spacetimes. In the present work we investigate the applicability of causal differencing to CADM, presenting the equations in a convenient way for such a goal and compare its application with the ADM approach in 1D.
Cite
@article{arxiv.gr-qc/0004065,
title = {Notes on causal differencing in ADM/CADM formulations: a 1D comparison},
author = {Luis Lehner and Mijan Huq and David Garrison},
journal= {arXiv preprint arXiv:gr-qc/0004065},
year = {2007}
}
Comments
11 pages, 6 figures. These notes illustrate how excision techniques already developed for ADM (in the form usually used in numerical relativity) codes can be straightforwardly applied in the so called `conformal ADM'. A comparison of the solutions obtained with both formulations is carried out highlighting when either formulation can yield better behaved evolutions