On Isometric Embeddings into Anti-de Sitter Space-times

Abstract

We show that any metric on $S^2$ with Gauss curvature $K\ge -\kappa$ admits a $C^{1,1}$-isometric embedding into the hyperbolic space with sectional curvature $-\kappa$. We also give a sufficient condition for a metric on $S^2$ to be isometrically embedded into anti-de Sitter spacetime with the prescribed cosmological time function.

27 pages

References in corpus (3)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Isometric embeddings into the Minkowski space and new quasi-local mass
• The Weyl problem with nonnegative Gauss curvature in hyperbolic space