Nonexistence of conformally flat slices of the Kerr spacetime

Details Nonexistence of conformally flat slices of the Kerr spacetime Nonexistence of conformally flat slices of the Kerr spacetime

2000-02-02

arxiv.org/abs/gr-qc/0002013v1

Phys.Rev. D61 (2000) 124011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 LaTeX pages; no figures; to be submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.61.124011

Initial data for black hole collisions are commonly generated using the Bowen-York approach based on conformally flat 3-geometries. The standard (constant Boyer-Lindquist time) spatial slices of the Kerr spacetime are not conformally flat, so that use of the Bowen-York approach is limited in dealing with rotating holes. We investigate here whether there exist foliations of the Kerr spacetime that are conformally flat. We limit our considerations to foliations that are axisymmetric and that smoothly reduce in the Schwarzschild limit to slices of constant Schwarzschild time. With these restrictions, we show that no conformally flat slices can exist.

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