The Great Escape: Tunneling out of Microstate Geometries

TL;DR

This paper calculates the quasi-normal frequencies of scalar perturbations in microstate geometries with capped BTZ-like throats, revealing universal long decay times and bounded energy decay, akin to ultracompact stars.

Contribution

It introduces a method to compute quasi-normal frequencies in non-separable wave equations for microstate geometries with capped BTZ throats, highlighting their universal decay properties.

Findings

Long decay times due to large redshifts in microstate geometries.

Energy decay bounded by (log t)^{-2}, similar to ultracompact stars.

Universal behavior of decay times across microstate geometries.

Abstract

We compute the quasi-normal frequencies of scalars in asymptotically-flat microstate geometries that have the same charge as a D1-D5-P black hole, but whose long BTZ-like throat ends in a smooth cap. In general the wave equation is not separable, but we find a class of geometries in which the non-separable term is negligible and we can compute the quasi-normal frequencies using WKB methods. We argue that our results are a universal property of all microstate geometries with deeply-capped BTZ throats. These throats generate large redshifts, which lead to exceptionally-low-energy states with extremely long decay times, set by the central charge of the dual CFT to the power of twice the dimension of the operator dual to the mode. While these decay times are extremely long, we also argue that the energy decay is bounded, at large $t$, by $(log~t)^{-2}$ and is comparable with the behavior of ultracompact stars, as one should expect for microstate geometries.