Toward stable 3D numerical evolutions of black-hole spacetimes

Three dimensional (3D) numerical evolutions of static black holes with excision are presented. These evolutions extend to about $8000M,$ where M is the mass of the black hole. This degree of stability is achieved by using growth-rate estimates to guide the fine tuning of the parameters in a multiparameter family of symmetric hyperbolic representations of the Einstein evolution equations. These evolutions were performed using a fixed gauge in order to separate the intrinsic stability of the evolution equations from the effects of stability-enhancing gauge choices.