  We consider the massless BTZ black hole and show that it is possible to take
its "near horizon" limit in two distinct ways. The first one leads to a null
self-dual orbifold of AdS3 and the second to a spacelike singular AdS3/Z_K
orbifold in the large K limit, the "pinching orbifold". We show that from the
dual 2d CFT viewpoint, the null orbifold corresponds to the p^+=0 sector of the
Discrete Light-Cone Quantisation (DLCQ) of the 2d CFT where a chiral sector of
the CFT is decoupled, while the pinching orbifold corresponds to taking an
infinite mass gap limit in both the right and left sectors of the 2d CFT,
essentially leaving us with the states L_0=\bar L_0=c/24 only. In the latter
case, one can combine the near horizon limit with sending the 3d Planck length
l_P to zero, or equivalently the dual CFT central charge c to infinity. We
provide preliminary evidence that in that case some nontrivial dynamics may
survive the limit.
