Can we distinguish whether black holes have singularities or not through echoes and light rings?

TL;DR

This paper investigates whether echoes and light rings can distinguish regular black holes from singular ones by analyzing quasinormal modes, null geodesics, and light ring structures in different black hole models.

Contribution

It provides a comparative analysis of quasinormal modes and light ring structures between regular and singular black holes, revealing potential observational signatures.

Findings

Echo signals may appear in singular black hole QNMs.

Regular black holes have only one light ring, while singular ones can have two.

The study links light ring structure to the presence of singularities.

Abstract

A recent work [Phys. Rev. D 111, 104040] shows that the curvature singularity of a black hole can vanish at a fine-tuned mass value, which implies that regular black holes could be special states in black hole evolution. We study the quasinormal modes (QNMs) of the Bardeen black hole and its singular counterparts under scalar and electromagnetic perturbations, employing the WKB method and time-domain analysis, respectively. The time-domain analysis results suggest that echo signals may emerge in the QNMs of singular black hole states. Furthermore, we investigate the null geodesics of these black holes. We find that a black hole with singularity may possess two light rings, whereas regular black holes consistently maintain only one light ring. Similar conclusions are also valid for the regular Hayward black hole and its singular counterparts.