# Thermal Decay without Information Loss in Horizonless Microstate Geometries

### Submission summary

 As Contributors: Ruben Monten Arxiv Link: https://arxiv.org/abs/1905.05194v2 (pdf) Date accepted: 2019-11-05 Date submitted: 2019-10-25 02:00 Submitted by: Monten, Ruben Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### 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 $\frac{1}{8}$-BPS asymptotically AdS$_3\,\times\,$S$^3$ 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$^3$ geometry of the black hole, but instead of having an event horizon, these geometries have a smooth highly-redshifted global-AdS$_3\,\times\,$S$^3$ 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$_3$ modulated by the BTZ response function. In position space, this translates into a sharp exponential black-hole-like decay for times shorter than $N_1 N_5$, followed by the emergence of evenly spaced "echoes from the cap," with period $\sim N_1 N_5$. Our result shows that horizonless microstate geometries can have the same thermal decay as black holes without the associated information loss.

### Ontology / Topics

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Published as SciPost Phys. 7, 063 (2019)

We would like to thank the referees for their thorough reading of our paper, for their very positive assessment and for their valuable suggestions. We have addressed their comments in this new version and we hope to be able to revisit their suggestions for further study in the future.

### List of changes

We have:
- corrected misprints such as Schrödinger (p.9 and onward),
- replaced the notation $\Psi_E$ by $\Psi_{ex}$ in order to avoid notational conflict with other conventions (eq(2.12) and onward),
- addressed the confusing statement $x \ll \infty$ (p.11),
- added the definitions of the Airy functions (p.11),
- explained the statement that $J_R = 1/2$ is the minimal value (p.27),
- commented briefly on the difficulty extending our method to flat space superstrata (p.5),
- added references to the Virgo/LIGO and Event Horizon Telescope publications.