Embedding spherical spacelike slices in a Schwarzschild solution

Abstract

Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothly embedded. One can use this result to show that any given Schwarzschild solution covers a significant subset of spherical superspace and these subsets form a sequence of nested domains as the Schwarzschild mass increases. This also demonstrates that spherical data offer an immediate counter example to the thick sandwich `theorem'.

References in corpus (3)

• Late time behaviour of the maximal slicing of the Schwarzschild black hole
• Optical scalars in spherical spacetimes
• The Constraints in Spherically Symmetric General Relativity I --- Optical Scalars, Foliations, Bounds on the Configuration Space Variables and the Positivity of the Quasi-Local Mass

Cited by in corpus (4)

• Geometry and Regularity of Moving Punctures
• Initial data sets for the Schwarzschild spacetime
• Asymptotics of solutions of a hyperbolic formulation of the constraint equations
• Spherical Spacelike Geometries in Static Spherically Symmetric Spacetimes: Generalized Painlevè-Gullstrand Coordinates, Foliation, and Embedding