  We study the matching between the Hawking temperature of a large class of
static D-dimensional black holes and the Unruh temperature of the corresponding
higher dimensional Rindler spacetime. In order to accomplish this task we find
the global embedding of the D-dimensional black holes into a higher dimensional
Minkowskian spacetime, called the global embedding Minkowskian spacetime
procedure (GEMS procedure). These global embedding transformations are
important on their own, since they provide a powerful tool that simplifies the
study of black hole physics by working instead, but equivalently, in an
accelerated Rindler frame in a flat background geometry. We discuss neutral and
charged Tangherlini black holes with and without cosmological constant, and in
the negative cosmological constant case, we consider the three allowed
topologies for the horizons (spherical, cylindrical/toroidal and hyperbolic).
