The great escape: tunneling out of 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.

Separability in consistent truncations

“…In this paper we have explored the interplay between consistent truncation and separability of the Hamilton-Jacobi equation in supergravity solutions. This work was stimulated by the discovery of separability in single-mode superstrata in [70][71][72][73], however, we have now shown that this was far from an accident: the structure of the uplifted metric of any consistent truncation is well-adapted to possible separability of both the wave equation and the Hamilton-Jacobi equation. This does not mean a generic consistent truncation will result in separability, and we have exhibited several, relatively simple examples where such separability fails.…”

“…Thus, if one restricts to single (1, 0, n) or (1, 1, n) the six-dimensional massless Hamilton-Jacobi equations will be fully separable. This separability has been extensively exploited in [70][71][72][73].…”

“…The first application was precisely the historical development that occurred with the (1, m, n) superstrata, [19][20][21], which motivated this work. Examples which give weight to the second application, include the microstate geometry probe calculations of [70][71][72][73] and the calculation of the spin 2 spectrum of the solution of section 6.1.1 in [74]. This later calculation was used as a check against the results coming directly from exceptional field theory using the methods of [75,76].…”

Black hole S-matrix for a scalar field

“…This is done by imposing appropriate matching conditions for the modes (associated to the transfer T-matrix) entering the Regge-Wheeler potential and those arising in the near horizon gravitational dynamics (associated to the near horizon scattering matrix). Such connection problems in the context of black holes have been studied in the past, a selection of these studies can be found in [32][33][34][35][36]. We perform this matching in two cases: Two-sided black hole.…”

“…17 Trapped modes have recently been discussed in the context of fuzzballs [35,36], but the difference with these works is that our background does contain a horizon. The mechanism of trapping is nevertheless analogous, due to the presence of an effective potential experienced by the modes, with a dip in the near horizon region.…”