Evolving Einstein's field equations with matter: The "hydro without hydro"test - art. no. 087501

We include matter sources in Einstein's held equations and show that our re cently proposed 3 + 1 evolution scheme can stably evolve strong-field solut ions. We insert in our code known matter solutions, namely the Oppenheimer- Volkoff solution for a static star and the Oppenheimer-Snyder solution for homogeneous dust sphere collapse to a black hole, and evolve the gravitatio nal field equations. We fmd that we ran evolve stably static, strong-field stars for arbitrarily long times and can follow dust sphere collapse accura tely well past black hale formation. These tests are useful diagnostics for fully self-consistent, stable hydrodynamical simulations in 3 + 1 general relativity. Moreover, they suggest a successive approximation scheme for de termining gravitational waveforms from strong-field sources dominated by lo ngitudinal fields, such as binary neutron stars: approximate quasi-equilibr ium models can serve as sources for the transverse field equations, which c an be evolved without having to re-solve the hydrodynamical equations ("hyd ro without hydro"). [S0556-2821(99)03118-5].