Asymptotically Flat Rotating Topological Stars

TL;DR

We address the problem of constructing rotating, horizonless microstate geometries in five-dimensional minimal supergravity that are smooth and asymptotically KK. The authors generate rotating solitons by applying sigma-model transformations to the Kerr-Taub-bolt seed, producing a discrete tower of rotating topological stars labeled by $k$ and characterized by a CFT-like data set $(k,\ell,N)$ with $|a|=\tfrac{k(r_+-r_-)}{2}$. The work advances the field by delivering explicit metrics and charges, analyzing regularity and ergoregions, computing multipole moments, and showing that these objects separate geodesic and scalar perturbations, enabling future dynamical studies; in a near-vacuum limit, they closely resemble a boosted Kerr black string while remaining horizonless, thereby providing concrete nonextremal microstate prototypes. This framework opens avenues for phenomenological exploration of gravitational signatures, stability, and the role of topological solitons in the gravitational phase space, with potential links to black-hole microstate physics in string theory.

Abstract

We construct a new class of smooth, horizonless, non-supersymmetric solutions in five-dimensional minimal supergravity, which we call rotating topological stars. Built from a Kerr-Taub-bolt geometry embedded in five dimensions, they constitute the first rotating generalization of the topological star compatible with both smoothness in the interior and standard Kaluza-Klein asymptotics, S$^1\times\mathbb{R}^{1,3}$. The solutions carry angular momentum, magnetic and electric charges, and form a discrete tower of states labeled by a primary quantum number controlling the spin. Remarkably, despite lying outside the black-hole extremality bound, they can approach arbitrarily closely (in conserved charges) the Kerr black string with a large boost along the fifth dimension, making them relevant prototypes for rotating and astrophysical black-hole microstates. We analyze their geometry in detail, including their gravitational multipoles that can significantly deviate from those of black holes and the presence of an ergoregion, and show that both geodesics and scalar perturbations separate, paving the way for analyzing their dynamics in future work.

Figures (1)

• Figure 1: Schematic description of a rotating topological star in $\mathbb{R}^{1,3}\times$S$^1$.