  We find necessary and sufficient conditions for existence of a locally
isometric embedding of a vacuum space-time into a conformally-flat 5-space. We
explicitly construct such embeddings for any spherically symmetric Lorentzian
metric in $3+1$ dimensions as a hypersurface in $R^{4, 1}$. For the
Schwarzschild metric the embedding is global, and extends through the horizon
all the way to the $r=0$ singularity. We discuss the asymptotic properties of
the embedding in the context of Penrose's theorem on Schwarzschild causality.
We finally show that the Hawking temperature of the Schwarzschild metric agrees
with the Unruh temperature measured by an observer moving along hyperbolae in
$R^{4, 1}$.
