  We investigate dipolar Bose-Einstein condensates in a complex external
double-well potential that features a combined parity and time-reversal
symmetry. On the basis of the Gross-Pitaevskii equation we study the effects of
the long-ranged anisotropic dipole-dipole interaction on ground and excited
states by the use of a time-dependent variational approach. We show that the
property of a similar non-dipolar condensate to possess real energy eigenvalues
in certain parameter ranges is preserved despite the inclusion of this
nonlinear interaction. Furthermore, we present states that break the PT
symmetry and investigate the stability of the distinct stationary solutions. In
our dynamical simulations we reveal a complex stabilization mechanism for
PT-symmetric, as well as for PT-broken states which are, in principle, unstable
with respect to small perturbations.
