Extending the lifetime of 3D black hole computations with a new hyperbolicsystem of evolution equations - art. no. 064017

We present a new many-parameter family of hyperbolic representations of Ein stein's equations, which we obtain by a straightforward generalization of p reviously known systems. We solve the resulting evolution equations numeric ally for a Schwarzschild black hole in three spatial dimensions, and find t hat the stability of the simulation is strongly dependent on the form of th e equations (i.e. the choice of parameters of the hyperbolic system), indep endent of the numerics. For an appropriate range of parameters we can evolv e a single three-dimensional black hole to t similar or equal to 600M - 130 0M, and we are apparently limited by constraint-violating solutions of the evolution equations. We expect that our method should result in comparable times for evolutions of a binary black hole system.