Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test

Details Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test

1999-02-09

arxiv.org/abs/gr-qc/9902024v1

Phys.Rev. D60 (1999) 087501

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Report

Scientific paper

10.1103/PhysRevD.60.087501

We include matter sources in Einstein's field equations and show that our recently proposed 3+1 evolution scheme can stably evolve strong-field solutions. 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 gravitational field equations. We find that we can evolve stably static, strong-field stars for arbitrarily long times and can follow dust sphere collapse accurately well past black hole 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 determining gravitational waveforms from strong-field sources dominated by longitudinal fields, like binary neutron stars: approximate quasi-equilibrium models can serve as sources for the transverse field equations, which can be evolved without having to re-solve the hydrodynamical equations (``hydro without hydro'').

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