Null geodesics, quasinormal modes and the correspondence with shadows in high-dimensional Einstein-Yang-Mills spacetimes

TL;DR

This paper explores the relationship between null geodesics, quasinormal modes, and shadow radii in high-dimensional Einstein-Yang-Mills black holes, revealing connections and unique features in five- and six-dimensional spacetimes.

Contribution

It establishes the link between photon sphere radii and horizon radii, and verifies the quasinormal mode-shadow correspondence in high-dimensional Einstein-Yang-Mills spacetimes.

Findings

Two branches of photon sphere radii in 5D, with only the outside branch satisfying circular geodesic conditions.

No spiral-like patterns in quasinormal mode frequencies on the complex plane.

Confirmed the quasinormal modes in the eikonal limit correspond to shadow radii.

Abstract

Null geodesics, quasinormal modes of a massless scalar field perturbation and the correspondence with shadow radii are investigated in the background spacetime of high-dimensional Einstein-Yang-Mills black holes. Based on the properties of null geodesics, we obtain the connection between the radius of a photon sphere and the radius of a horizon in the five- and six-dimensional Einstein-Yang-Mills spacetimes. Especially in the five-dimensional case, there exist two branches for the radius of a photon sphere, but only the branch outside the event horizon satisfies the condition of circular null geodesics. Moreover, we find no reflecting points of shadow radii and no spiral-like shapes on the complex plane of quasinormal frequencies and verify the correspondence between the quasinormal modes in the eikonal limit and shadow radii in high-dimensional Einstein-Yang-Mills spacetimes.