Integrability and Black-Hole Microstate Geometries

TL;DR

This paper investigates specific supergravity solutions called superstrata that mimic black holes but are horizonless, revealing integrability properties and separability of wave equations, which have implications for understanding black-hole microstates.

Contribution

It demonstrates integrability and separability in certain superstrata solutions, linking geometric symmetries to the physics of black-hole microstate geometries.

Findings

Null geodesic problem is integrable for an infinite family of solutions.

Massless scalar wave equation is separable in these backgrounds.

Some solutions exhibit conformal Killing tensors only when angular momentum is zero.

Abstract

We examine some recently-constructed families of asymptotically-AdS$_3 \times$S$^3$ supergravity solutions that have the same charges and mass as supersymmetric D1-D5-P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S$^3$ down to a (2+1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries.