Inscribing geodesic circles on the face of the superstratum

Abstract

We use families of circular null geodesics as probes of a family of microstate geometries, known as $(1,0,n)$ superstrata. These geometries carry a left-moving momentum wave and the behavior of some of the geodesic probes is very sensitive to this background wave. The left-moving geodesics behave like BPS particles and so can be placed in circular orbits anywhere in the geometry and actually "float" at fixed radius and angle in the three-dimensional "capped BTZ" geometry. The right-moving geodesics behave like non-BPS particles. We show that they provide a simple geometric characterization of the black-hole bound: when the momentum charge of the geometry is below this bound, such geodesics can be placed anywhere, but exceeding the bound, even by a small amount, means these geodesics are restricted to the deep interior of the geometry. We also show that for left-moving string probes, the tidal forces remain comparable with those of global AdS$_3$. Nevertheless, for some of these probes, the "bumps" in the geometry induce an oscillatory mass term and we discuss how this can lead to chaotic scrambling of the state of the string.