  We show that any metric on $S^2$ with Gauss curvature $K \geq -\kappa$ 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.
