Thermal decay without information loss in horizonless microstate geometries

Abstract

We develop a new hybrid WKB technique to compute boundary-to-boundary scalar Green functions in asymptotically-AdS backgrounds in which the scalar wave equation is separable and is explicitly solvable in the asymptotic region. We apply this technique to a family of six-dimensional \frac{1}{8}18-BPS asymptotically AdS_3\,\times\,3×S^33 horizonless geometries that have the same charges and angular momenta as a D1-D5-P black hole with a large horizon area. At large and intermediate distances, these geometries very closely approximate the extremal-BTZ\,\times\,×S^33 geometry of the black hole, but instead of having an event horizon, these geometries have a smooth highly-redshifted global-AdS_3\,\times\,3×S^33 cap in the IR. We show that the response function of a scalar probe, in momentum space, is essentially given by the pole structure of the highly-redshifted global-AdS_33 modulated by the BTZ response function. In position space, this translates into a sharp exponential black-hole-like decay for times shorter than N_1 N_5N1N5, followed by the emergence of evenly spaced “echoes from the cap,” with period \sim N_1 N_5∼N1N5. Our result shows that horizonless microstate geometries can have the same thermal decay as black holes without the associated information loss.