A recent proposal by Ryu and Takayanagi for a holographic interpretation of
entanglement entropy in conformal field theories dual to supergravity on
anti-de Sitter (adS) is generalized to include entanglement entropy of black
holes living on the boundary of adS. The generalized proposal is verified in
boundary dimensions d=2 and d=4 for both the UV divergent and UV finite
terms. In dimension d=4 an expansion of entanglement entropy in terms of size
L of the subsystem outside the black hole is considered. A new term in the
entropy of dual strongly coupled CFT, which universally grows as L2lnL and
is proportional to the value of the obstruction tensor at the black hole
horizon, is predicted.Comment: 5 pages; minor typos corrected, minor changes in text. Version
accepted for publication in Phys. Rev. Let