Regularization of spherical and axisymmetric evolution codes in numerical relativity

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dc.creatorRuiz, Milton
dc.creatorAlcubierre, Miguel
dc.creatorNunez, Dario
dc.date2007-06-06
dc.date2007-09-11
dc.date.accessioned2026-07-07T11:16:40Z
dc.date.available2026-07-07T11:16:40Z
dc.descriptionSeveral interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne and Stewart and present a simple procedure to regularize the equations both in spherical and axi-symmetric spaces. We explicitly show the regularity of the evolution equations, describe the corresponding numerical code, and present several examples clearly showing the regularity of our evolutions.
dc.description11 pages, 9 figures. Several changes. Main corrections are in eqs. (2.12) and (5.14). Accepted in Gen. Rel. Grav
dc.identifierhttps://arxiv.org/abs/0706.0923
dc.identifierhttp://arxiv.org/abs/0706.0923
dc.identifierGen.Rel.Grav.40:159-182,2008
dc.identifierdoi:10.1007/s10714-007-0522-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/192751
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleRegularization of spherical and axisymmetric evolution codes in numerical relativity
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