Causal differencing in ADM and conformal ADM formulations: A comparison inspherical symmetry - art. no. 084016

Black hole excision is at present the most promising approach to deal with the singularities in black hole spacetimes. The implementation of this tech nique is done through carefully designed algorithms that exploit the causal structure of the spacetime in the black hole region. Causal differencing h as shown to be one of the promising algorithms. To date, it has only been a ctively implemented in the Arnowitt-Deser-Misner (ADM) and Einstein-Bianchi 3 + 1 formulations of the Einstein equations. Recently, an approach closel y related to the ADM one, commonly referred to as "conformal ADM" (CADM) me thod has shown excellent results when modeling waves on Rat spacetimes and black hole spacetimes where singularity avoiding slices are used to deal wi th the singularity. In these cases, the use of the CADM method 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 the CADM method, presenting th e equations in a convenient way for such a task. We investigate whether the causal differencing implementation already developed for the ADM system ca n be extended to the CADM one.