Towards stable evolutions of excised black hole spacetimes via the ADM equations: A spherically symmetric test - art. no. 044037

Within the numerical relativity community, much effort has been devoted to simulate the coalescence of black hole binaries. A key problem in attemptin g such a simulation is the handling of the singularity present in each hole . A very promising approach to address this issue is the excision of the si ngularities from the computational domain. However, to date there have been only a few restricted examples in the literature showing that this approac h yields long-term stable simulations in 3+1 formulations. It has been argu ed that the form of the Einstein field equations normally used, namely, the Arnowitt-Deser-Misner (ADM) equations, when applied to black hole excision , could be the cause of instabilities. By means of perturbative and numeric al studies in spherical symmetry [one-dimensional (1D)]. we show that succe ssful numerical solutions of excised, single black hole spacetimes can be c onstructed with the ADM formulation of Einstein equations if the appropriat e choice of gauge or coordinate conditions is made. Preliminary 3D results are consistent with the 1D studies.