Towards stable evolutions of excised black hole spacetimes via the ADM equations: A spherically symmetric test

Within the numerical relativity community, much effort has been devoted to simulate the coalescence of black hole binaries. A key problem in attempting 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 singularities from the computational domain. However, to date there have been only a few restricted examples in the literature showing that this approach yields long-term stable simulations in 3+1 formulations. It has been argued 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 numerical studies in spherical symmetry [one-dimensional (1D)], we show that successful numerical solutions of excised, single black hole spacetimes can be constructed with the ADM formulation of Einstein equations if the appropriate choice of gauge or coordinate conditions is made. Preliminary 3D results are consistent with the 1D studies.