Topological Stars and scalar wave equation: Exact resummation of the renormalized angular momentum in the eikonal limit

TL;DR

This paper establishes a precise connection between the renormalized angular momentum in topological stars and geodesic actions, providing an exact hypergeometric resummation that extends previous Schwarzschild results.

Contribution

It introduces an exact hypergeometric resummation of the renormalized angular momentum for topological stars, generalizing earlier Schwarzschild findings and linking it to geodesic actions.

Findings

Exact resummation of angular momentum in topological stars

Connection between angular momentum and geodesic radial action

Generalization of Schwarzschild case results

Abstract

We show that for a Topological Star the renormalized angular momentum parameter, $\nu$, appearing in the Mano-Suzuki-Takasugi-type or in the quantum-Seiberg-Witten-type approaches of the perturbation equations, has 1) a direct link with the geodesic radial action computed along the null orbits of the background and 2) admits an exact resummation in terms of hypergeometric functions, generalizing previous results valid in the Schwarzschild case, see Ref.[arXiv:2504.07862 [hep-th]].