  It is shown that optical geometry of the Reissner-Nordstrom exterior metric
can be embedded in a hyperbolic space all the way down to its outer horizon.
The adopted embedding procedure removes a breakdown of flat-space embeddings
which occurs outside the horizon, at and below the Buchdahl-Bondi limit
(R/M=9/4 in the Schwarzschild case). In particular, the horizon can be captured
in the optical geometry embedding diagram. Moreover, by using the compact
Poincare ball representation of the hyperbolic space, the embedding diagram can
cover the whole extent of radius from spatial infinity down to the horizon.
Attention is drawn to advantages of such embeddings in an appropriately curved
space: this approach gives compact embeddings and it distinguishes clearly the
case of an extremal black hole from a non-extremal one in terms of topology of
the embedded horizon.
