Asymptotically-flat supergravity solutions deep inside the black-hole regime

Abstract

Abstract:We construct an infinite family of smooth asymptotically-flat supergravity solutions that have the same charges and angular momenta as general supersymmetric D1-D5-P black holes, but have no horizon. These solutions resemble the corresponding black hole to arbitrary accuracy outside of the horizon: they have asymptotically flat regions, AdS 3 × S 3 throats and very-near-horizon AdS 2 throats, which however end in a smooth cap rather than an event horizon. The angular momenta of the solutions are general, and in particular can take arbitrarily small values. Upon taking the AdS 3 × S 3 decoupling limit, we identify the holographically-dual CFT states.

Little strings, long strings, and fuzzballs

“…In the AdS/CFT context, and perhaps more broadly, gravity is a collective mode of the underlying microscopics, whose emergent diffeomorphism symmetry determines the outcome. 21 One can check that the density of states of these two configurations flow into one another according to the standard spectral flow relations of the spacetime CFT, which on the gravity side of the duality is simply a large gauge transformation that mixes AdS 3 and S 3 angular coordinates. Both objects have horizon topology S 3 × S 1 , so it is consistent that they flow into one another.…”

“…This result suggests that once again the route to the black hole phase proceeds via a process in which the background sheds its angular momentum and the cap descends to a redshift where the entropic degrees of freedom become light enough to play a significant role. Superstrata can support a deep AdS 2 throat and an approximate BTZ geometry via coherent supergravity waves on top of a two-charge supertube background [21]. The fully nonlinear field equations are solved, with the wave profile tuned to avoid singularities and other pathologies such as closed timelike curves.…”

Counting superstrata

“…If we take the flow parameter η = −1/2, NS states get mapped into R states. However, to match the convention of charges to that in the literature [29,42,44], we further flip the sign of the SU (2) L charge, as j → −j. So, the map from NS to R that we will be using is…”

“…Based on these developments, the first examples of superstrata were explicitly constructed in [29], providing a proof of their existence. After that, superstratum solutions have been generalized in many ways [41][42][43][44][45][46][47], and a number of checks of their proposed AdS/CFT dictionary were carried out [37,48]. By now it is fair to say that we have a pretty good picture of possible superstrata solutions, although explicit expressions have been found only for a limited class of solutions.…”

Correlation functions in the D1-D5 orbifold CFT

“…Early discussions of (non-generic) microstates for macroscopic black holes can be found in [18][19][20][21][22][23][24][25]. Recent constructions of microstates illustrate more generic features, using concepts such as superstrata, see for example [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]; there is ongoing study of what fraction of the black hole microstates such constructions can represent.…”