A note on time-symmetric hypersurfaces in the Schwarzschild geometry

Abstract

In this note we show that any inextensible time-symmetric space-like hypersurface of differentiability class $C^k$, $k\ge 2$ isometrically embedded in the maximal Schwarzschild geometry must intersect the bifurcation sphere.

Proof of corollary 2 extended to include hypersurfaces with null regions. Some additional considerations in section 4 dealing with hypersurfaces of arbitrary causal character added. References added, To appear in classical and quantum gravity

References in corpus (2)

• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes