TREATING INSTABILITIES IN A HYPERBOLIC FORMULATION OF EINSTEINS EQUATIONS - ART. NO. 044020

We have recently constructed a numerical code that evolves a spherical ly symmetric spacetime using a hyperbolic formulation of Einstein's eq uations. For the case of a Schwarzschild black hole, this code works w ell at early times, but quickly becomes inaccurate on a time scale of( 10-100)M, where M is the mass of the hole. We present an analytic meth od that facilitates the detection of instabilities. Using this method, we identify a term in the evolution equations that leads to a rapidly growing mode in the solution. After eliminating this term from the ev olution equations by means of algebraic constraints, we can achieve Ge e evolution for times exceeding 10 000M. We discuss the implications f or three-dimensional simulations. [S0556-2821(98)00318-X].