Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-03-27
Phys.Rev.D64:084013,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
20 pages, 9 figures
Scientific paper
10.1103/PhysRevD.64.084013
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove the singularities. We show that, for the case of a single black hole in spherical symmetry, it is possible to circumvent these problems by adding to the evolution equations terms involving the constraints, thus adjusting the standard ADM system. We investigate the effect that the choice of the lapse and shift has on the stability properties of numerical simulations and thus on the form of the added constraint term. To facilitate this task, we introduce the concept of quasi well-posedness, a version of well-posedness suitable for ADM-like systems involving second-order spatial derivatives.
Kelly Bernard
Laguna Pablo
Lockitch Keith
Pullin Jorge
Schnetter Erik
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