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GR: Fachverband Gravitation und Relativitätstheorie

GR 16: Hauptvorträge: Numerische Relativitätstheorie und Wurmlöcher

GR 16.1: Hauptvortrag

Freitag, 1. März 2013, 09:15–10:00, HS 6

Numerical evolution of the Einstein equations to future null infinity — •Oliver Rinne — Albert-Einstein-Institut

In numerical simulations of isolated systems, one usually adopts the Cauchy formulation of general relativity and foliates spacetime by spacelike hypersurfaces that are truncated at a finite distance. Boundary conditions must be imposed so that the resulting initial-boundary value problem is well posed and, ideally, the artificial boundary is transparent to gravitational radiation. However, the latter is only defined unambiguously at future null infinity (Scri+) and so a far more elegant solution is to include Scri+ in the numerical domain. This can be accomplished by a conformal transformation of the metric combined with a compactifying coordinate transformation. With Vince Moncrief we have developed a constrained ADM-like formulation of the Einstein equations on hypersurfaces of constant mean curvature approaching Scri+. Although the equations contain terms that are formally singular at Scri+, these can nevertheless be evaluated in a regular way. Numerical results based on this formulation include evolutions of perturbed vacuum axisymmetric black holes and studies of late-time power-law tails of scalar and Yang-Mills fields coupled to the Einstein equations in spherical symmetry.