  For spacetimes that are not asymptotic to anti-de Sitter Space (non AAdS), we
adapt the Lewkowycz-Maldacena procedure to find the holographic entanglement
entropy. The key observation, which to our knowledge is not very well
appreciated, is that asymptotic boundary conditions play an essential role on
extending the replica trick to the bulk. For non AAdS, we expect the following
three main modifications: (1) the expansion near the special surface has to be
compatible with the asymptotic expansion; (2) periodic conditions are imposed
to coordinates on the phase space with diagonalized symplectic structure, not
to all fields appearing in the action; (3) evaluating the entanglement
functional using the boundary term method amounts to evaluating the
presymplectic structure at the special surface, where some additional exact
form may contribute. An explicit calculation is carried out for
three-dimensional warped anti-de Sitter spacetime (WAdS3) in a consistent
truncation of string theory, the so-called S-dual dipole theory. It turns out
that the generalized gravitational entropy in WAdS3 is captured by the least
action of a charged particle in WAdS3 space, or equivalently, by the geodesic
length in an auxiliary AdS3. Consequently, the bulk calculation agrees with the
CFT results, providing another piece of evidence for the WAdS3/CFT2
correspondence.
