The compactification of initial data on constant mean curvature time slices in spherically symmetric spacetimes

Details The compactification of initial data on constant mean curvature time slices in spherically symmetric spacetimes The compactification of initial data on constant mean curvature time slices in spherically symmetric spacetimes

2001-07-04

arxiv.org/abs/gr-qc/0107016v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

Conformal mappings of surfaces of constant mean curvature onto compact bounded background spaces are constructed for Minkowski space-time and for Schwarzschild black hole spacetimes. In the black hole example, it is found that initial data on these CMC surfaces can be regular on the compact background space only when a certain condition is satisfied. That condition implies that the shift vector points inward from all parts of the boundary of the compact background. It also implies that the second fundamental form of these surfaces can never be isotropic when black holes are present.

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