Smooth Horizonless Geometries Deep Inside the Black-Hole Regime

We construct the first family of horizonless supergravity solutions that have the same mass, charges, and angular momenta as general supersymmetric rotating $D1\text{−}D5\text{−}P$ black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically dual states in the $\mathcal{N}=(4,4)$ $D1\text{−}D5$ orbifold conformal field theory (CFT). Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.

Figure 1

Sketch of the superstratum spatial geometry in the $r\text{−}y$ plane, compared to the extremal BTZ geometry.