We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasilinear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between. Proofs of well-posed evolution and boundary algorithms for a second differential order treatment of the system are given for the separate pieces underlying the finite-difference problem. These are implemented in a numerical code which gives accurate long term simulations of the quasilinear excision problem. Excitation of long wavelength exponential modes, which are latent in the problem, are suppressed using conservation laws for the discretized system. The techniques are designed to apply directly to recent codes for the Einstein equations based upon the harmonic formulation.

• Received 22 December 2004

DOI:https://doi.org/10.1103/PhysRevD.71.104035