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Can we distinguish whether black holes have singularities or not through echoes and light rings?
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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.
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Spectrum instability and greybody factor stability for parabolic approximation of Regge-Wheeler potential
Replacing the Regge-Wheeler potential by piecewise parabolas makes quasinormal-mode spectra unstable, with long-lived overtones, while greybody factors stay close to the exact Schwarzschild result.
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