Abstract
We build the first family of smooth bubbling microstate geometries that are asymptotic to the near-horizon region of extremal five-dimensional Kerr black holes (NHEK). These black holes arise as extremal non-supersymmetric highly-rotating D1-D5- P solutions in type IIB string theory on T4×S1. Our solutions are asymptotically NHEK in the UV and end in the IR with a smooth cap. In the context of the Kerr/CFT correspondence, these bubbling geometries are dual to pure states of the 1+1 dimensional chiral conformal field theory dual to NHEK. Since our solutions have a bubbling structure in the IR, they correspond to an IR phase of broken conformal symmetry, and their existence supports the possibility that all the pure states whose counting gives the Kerr black hole entropy correspond to horizonless bulk configurations.
Highlights
The black hole quantum state is a vector in a Hilbert space spanned by microstates approximated by smooth horizonless geometries that have the same mass, angular momentum and charges as the corresponding black hole
Its near-horizon geometry is a squashed S3 (SqS3) over warped AdS3 factor (WAdS3) which corresponds to a NHEK geometry, but the warp factor is constant, unlike for the NHEK solution in four dimensions
We identify the periodicities at infinity of WAdS3×SqS3 or NHEK and impose the absence of conical singularities at the centers
Summary
We work in the context of type IIB string theory on a T 4 × S1. The five-dimensional black hole solutions can be seen as six-dimensional black string solutions. M = 2 a2 c21 + s21 + c25 + s25 + c2p + s2p , JR = 0, JL = 4 a3 (c1c5cp + s1s5sp) , QI = 4 a2 sI cI , I = 1, 5, p,. The Bekenstein-Hawking entropy and the left and right temperatures are SBH = 2π JL2 − Q1Q5Qp = 8π a3 (c1c5cp − s1s5sp) , TL = 0,. The coordinate ris the radial coordinate of the four-dimensional base space defined by rand the three angles θ, φ, ψand yis the KK direction. The periodicities of the angles y, ψand φare.
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