Correspondence of eikonal quasinormal modes and unstable fundamental photon orbits for Kerr-Newman black hole

TL;DR

This paper establishes an exact correspondence between eikonal quasinormal modes and unstable photon orbits in Kerr-Newman black holes, revealing that their frequencies relate to orbital and Lyapunov exponents in the eikonal limit.

Contribution

It demonstrates the EQNM/UFPO correspondence for Kerr-Newman black holes, extending previous Kerr results and showing the decoupling of perturbations in the eikonal limit.

Findings

EQNMs are decoupled into Schrödinger-like equations.

Exact EQNM/UFPO correspondence is established.

Frequencies relate to orbital and Lyapunov exponents.

Abstract

In this work, we study the relation of the eikonal quasinormal modes (EQNMs) and the unstable fundamental photon orbits (UFPOs) in the Kerr-Newman spacetime. We find that in the eikonal limit the gravitational and electromagnetic perturbations of the Kerr-Newman black hole are naturally decoupled, and a single one-dimensional Schr\"odinger-like equation encoding the QNM spectrum can be derived. We then show that the decoupled Teukolsky master equation and the Klein-Gordon equation for the massless scalar field in the Kerr-Newman spacetime are of the same form in the eikonal limit. As a direct consequence, taking into account of the boundary conditions for EQNMs we show an exact correspondence between EQNMs and UFPOs, that is, EQNM/UFPO correspondence. More precisely, similar to the Kerr case, the real part of EQNM's frequency is a linear combination of the precessional and (polar) orbital frequencies, while the imaginary part of the frequency is proportional to the Lyapunov exponent of the UFPO.