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arXiv · 1310.4699

Axisymmetric constant mean curvature slices in the Kerr space-time

David Schinkel·Rodrigo Panosso Macedo·Marcus Ansorg
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Abstract

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.

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David Schinkel, Rodrigo Panosso Macedo, Marcus Ansorg. 2013-10-17. Axisymmetric constant mean curvature slices in the Kerr space-time. https://doi.org/10.1088/0264-9381/31/7/075017

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