A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations

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dc.creatorKelly, Bernard
dc.creatorLaguna, Pablo
dc.creatorLockitch, Keith
dc.creatorPullin, Jorge
dc.creatorSchnetter, Erik
dc.creatorShoemaker, Deirdre
dc.creatorTiglio, Manuel
dc.date2001-03-27
dc.date.accessioned2026-07-07T10:51:47Z
dc.date.available2026-07-07T10:51:47Z
dc.descriptionNumerical 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.
dc.description20 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/gr-qc/0103099
dc.identifierhttp://arxiv.org/abs/gr-qc/0103099
dc.identifierPhys.Rev.D64:084013,2001
dc.identifierdoi:10.1103/PhysRevD.64.084013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184938
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations
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