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We first review spacelike stretched warped AdS$_3$ and we describe its blackhole quotients by using accelerating and Poincar\'e coordinates. We thendescribe the maximal analytic extension of the black holes and present theircausal diagrams. Finally, we calculate spacetime limits of the black hole phasespace $(T_R,T_L)$. This is done by requiring that the identification vector$\partial_\theta$ has a finite non-zero limit. The limits we obtain are theself-dual solution in accelerating or Poincar\'e coordinates, dependingrespectively on whether the limiting spacetimes are non-extremal or extremal,and warped AdS with a periodic proper time identification.

From accelerating and Poincar\'e coordinates to black holes in spacelike warped AdS$_3$, and back