Ma. Scheel et al., TREATING INSTABILITIES IN A HYPERBOLIC FORMULATION OF EINSTEINS EQUATIONS - ART. NO. 044020, Physical review. D. Particles and fields, 5804(4), 1998, pp. 4020
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].