Supersymmetric warped AdS in extended topologically massive supergravity

We determine the most general form of off-shell N=(1,1)N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS3AdS3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS3AdS3. This occurs when the coefficient of the Lorentz–Chern–Simons term is related to the AdS   radius by μℓ=2μℓ=2. We find that the spacelike-squashed AdS3AdS3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoids closed timelike curves.