$T\bar T$, Black Holes and Negative Strings

Understand

String theory on $AdS_3$ has a solvable single-trace irrelevant deformation that is closely related to $T\bar T$.

• For one sign of the coupling, it leads to an asymptotically linear dilaton spacetime, and a corresponding Hagedorn spectrum.
• For the other, the resulting spacetime has a curvature singularity at a finite radial location, and an upper bound on the energies of states.
• Beyond the singularity, the signature of spacetime is flipped and there is an asymptotically linear dilaton boundary at infinity.