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

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.

v1: 10 pages, 6 figures; v2: clarifications added and references adjusted; v3: 14 pages, clarifications, 6 tables and one reference added, final version to appear in Physical Review D

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