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

2001/07/04 by Robert H. Gowdy, Gowdy, Robert H.
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc

paper · pdf · doi:10.48550/arxiv.gr-qc/0107016

9 pages

arxiv created 2001/07/04 · openalex publication_date 2001/07/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Black hole initial data with a horizon of prescribed intrinsic and extrinsic geometry
• When Do Spacetimes Have Constant Mean Curvature Slices?
• Asymptotically Flat Initial Data for Gravitational Wave Spacetimes, Conformal Compactification and Conformal Symmetry
• Rigidity of stable marginally outer trapped surfaces in initial data sets
• Detecting Event Horizons and Stationary Surfaces