  A proposal to describe gravity duals of conformal theories with boundaries
(AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However
interesting solutions describing field theories at finite temperature and
charge density are still lacking. In this paper we describe a class of theories
with boundary, which admit black hole type gravity solutions. The theories are
specified by stress-energy tensors that reside on the extensions of the
boundary to the bulk. From this perspective AdS/BCFT appears analogous to the
fluid/gravity correspondence. Among the class of the boundary extensions there
is a special (integrable) one, for which the stress-energy tensor is
fluid-like. We discuss features of that special solution as well as its
thermodynamic properties.
