Berlin 2015 – scientific programme

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GR: Fachverband Gravitation und Relativitätstheorie

GR 16: Numerical Relativity

GR 16.5: Talk

Thursday, March 19, 2015, 16:50–17:10, H 2013

Axisymmetric constant mean curvature slices in the Kerr space-time — •David Schinkel, Rodrigo Panosso Macedo, and Marcus Ansorg — Theoretisch-Physikalisches Institut, Jena, Germany

Recently, there have been efforts to solve Einstein's equation in the context of a conformal compactification of space-time. Of particular importance in this regard are the so called CMC-foliations, characterized by spatial hyperboloidal hypersurfaces with a constant extrinsic mean curvature K. However, although of interest for general space-times, CMC-slices are known explicitly only for the spherically symmetric Schwarzschild metric. This work is devoted to numerically determining axisymmetric CMC-slices within the Kerr solution. We construct such slices outside the black hole horizon through an appropriate coordinate transformation in which an unknown auxiliary function A is involved. The condition K=const throughout the slice leads to a nonlinear partial differential equation for the function A, which is solved with a pseudo-spectral method. The results exhibit exponential convergence, as is to be expected in a pseudo-spectral scheme for analytic solutions. As a by-product, we identify CMC-slices of the Schwarzschild solution which are not spherically symmetric.