  We show that the entropy of D--dimensional Schwarzschild black holes are
given by the entanglement entropy of a boundary of global $AdS_2$ space that
lives at asymptotic infinity. We dimensionally reduce General Relativity to two
dimensions which leads to 2D dilatonic gravity which has black hole solutions
with the same thermodynamics as D--dimensional Schwarzschild black holes. These
dilatonic black holes can be transformed into certain $AdS_2$ black holes by
Weyl transformations which are symmetries of the theory that preserve the
thermodynamics. In the asymptotic limit, the $AdS_2$ black holes become global
$AdS_2$ which can be described by two entangled $AdS_2$ Rindler spaces. The
entanglement entropy of a single $AdS_2$ Rindler space reproduces the
Schwarzschild black hole entropy.
