Assuming U(1) symmetry of solutions we construct a fully constrained scheme for Einstein equations on compact spatial domains with S2 x S1 and S3 topology.
Performing Geroch reduction and choosing appropriate gauge we rewrite Einstein equations into a system of elliptic and hyperbolic equations which are suitable for numerical computations. Following the approach of Beyer, Escobar and Frauendiener we use spin‐weighted spherical harmonics to deal with the singularities of spherical polar coordinates. We apply the scheme to rotating cosmologies initial data with
U(1)xU(1) symmetry found by Bizoń, Simon and Pletka.
Jerzy Knopik (Vienna): Gowdy spacetimes with a positive cosmological constant
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Foto: Barbara Mair