Quasinormal modes-shadow correspondence for rotating regular black holes

TL;DR

This paper extends the relationship between quasinormal modes and shadow radii from spherically symmetric to more general rotating black holes, enabling new tests of gravity through gravitational waves and imaging.

Contribution

It generalizes the QNM-shadow radius correspondence to a broader class of rotating black holes, including those generated by the Newman-Janis algorithm, under specific mathematical conditions.

Findings

The correspondence holds for rotating Bardeen and Hayward black holes.

Conditions on the Hamilton-Jacobi and Klein-Gordon equations are necessary for the correspondence.

The results enable potential multi-messenger tests of fundamental physics.

Abstract

Eikonal quasinormal modes (QNMs) of black holes (BHs) and parameters of null geodesics, ultimately tied to the appearance of BHs to external observers, are known to be related, and the eikonal QNM-BH shadow radii correspondence has been extensively studied for spherically symmetric BHs. The extension to rotating BHs is non-trivial, and has been worked out only for equatorial ($m=\pm\ell$) QNMs, or for general modes but limited to the Kerr metric. We extend the QNM-shadow radius correspondence to more general rotating space-times, and argue that the requirements for it to hold amount to conditions on the separability of the Hamilton-Jacobi equation for null geodesics and the Klein-Gordon equation. Metrics obtained by the Newman-Janis algorithm enjoy these conditions, provided certain mathematical requirements are imposed on the line element. We explicitly verify the correspondence for the rotating Bardeen and Hayward regular BHs, both of which satisfy the separability requirements. Our findings show that the QNM-shadow radius correspondence holds for a wide range of axisymmetric space-times beyond Kerr. This paves the way to potential strong-field multi-messenger tests of fundamental physics by hearing (via gravitational wave spectroscopy) and seeing (via VLBI imaging) BHs, although substantial improvements relative to the current observational sensitivity are required to make this possible.