Quasinormal modes of the generalized JMN naked singularity using exact WKB analysis

TL;DR

This paper analyzes the quasinormal modes of the generalized JMN naked singularity spacetime using exact WKB methods, revealing unique Stokes geometry features that distinguish it from black holes.

Contribution

It introduces an exact WKB approach to identify topological Stokes features as signatures of naked singularities, advancing the understanding of compact object perturbations.

Findings

Identified bow-shaped deformation of Stokes curves near the singularity.

Linked the Stokes topology to the logarithmic branch point at r=0.

Demonstrated the potential of Stokes geometry to differentiate black holes from naked singularities.

Abstract

In this paper, we study the quasinormal modes of the generalized Joshi-Malafarina-Narayan (JMN) naked singularity spacetime using the exact Wentzel-Kramers-Brillouin (WKB) method. Working in the complex radial plane, we construct the exact WKB momentum function, determine its turning points, and compute the associated Stokes geometry for representative quasinormal mode (QNM) frequencies. We obtained a bow-shaped deformation of Stokes curves on the side of the complex plane containing the central singularity in JMN spacetime. We show analytically that this structure originates from the logarithmic branch-point singularity of the WKB phase at $(r = 0)$, which is absent in Schwarzschild spacetime. This establishes the bow-shaped Stokes topology as a direct signature of the naked singularity in the global analytic structure of the perturbation equation. Our results demonstrate that exact WKB analysis provides a powerful framework for probing the analytic structure of compact objects, and suggest that topological features of Stokes geometry may offer a new avenue for distinguishing black holes from horizonless alternatives.