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