Relating Black Hole Shadow to Quasinormal Modes for Rotating Black Holes

TL;DR

This paper establishes a theoretical link between the black hole shadow and quasinormal modes for rotating Kerr black holes, extending previous non-rotating results and suggesting observational tests with future detectors.

Contribution

It introduces a novel mapping between black hole shadows and quasinormal modes for rotating black holes, expanding understanding of their observable properties.

Findings

Shadow-to-quasinormal mode mapping for Kerr black holes.

Bound on the ratio m/(l+1/2) for modes.

Potential for observational testing with future detectors.

Abstract

In this work, we explore the connection between the critical curves ("shadows") and the quasinormal mode frequencies (in the eikonal limit) of Kerr black holes. This mapping has been previously established for non-rotating black holes. We show that, the shadow seen by an distant observer at a given inclination angle, can be mapped to a family of quasinormal modes with $m/(\ell+1/2)$ bounded within certain range, where $m$ is is azimuthal node number and $\ell$ is the angular node number. We discuss the possibility of testing such relation with space-borne gravitational wave detectors and the next-generation Event Horizon Telescope.