Analytical correspondence between shadow radius and black hole quasinormal frequencies

TL;DR

This paper derives an analytical relation linking black hole shadow radius to quasinormal frequencies at the eikonal limit, verified across different black hole families, enhancing understanding of black hole observational signatures.

Contribution

It introduces a new analytical relation between shadow radius and quasinormal modes, validated for black holes in four and higher dimensions.

Findings

Established an analytical relation between shadow radius and quasinormal frequencies.

Validated the relation for black holes in 4D and D dimensions.

Enhanced the theoretical understanding of black hole shadows and oscillations.

Abstract

We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius. We verify this correspondence with two black hole families in $4$ and $D$ dimensions, respectively.