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

Yang Guo,Yan-Gang Miao

doi:10.1103/physrevd.102.084057

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.

Highlights

Quasinormal modes (QNMs) are usually used to depict the stability of black holes that are perturbed by an external field or by the metric of black hole spacetimes, and they contain the information of gravitational waves
We have studied the null geodesics and the correspondence between QNMs in the eikonal limit and shadow radii for high-dimensional EYM black holes
Two branches of the radius of a photon sphere exist, but only the one outside the event horizon satisfies the conditions of circular null geodesics

Summary

INTRODUCTION

Quasinormal modes (QNMs) are usually used to depict the stability of black holes that are perturbed by an external field or by the metric of black hole spacetimes, and they contain the information of gravitational waves. We make a brief review on the correspondence between QNMs and other important issues, such as spacelike geodesics, phase transitions, and null geodesics, which naturally gives our motivation and aim of the present paper It has been proposed [12,13] that the QNM frequencies in the large black hole mass limit are determined by the spacelike geodesics with the boundary of the Penrose diagram, based on which the quantum aspect of gravity behind horizons can be probed in the context of the gauge/gravity duality. This relation between QNMs and phase transitions gives an opportunity to probe [15] the thermodynamics and dynamics of black holes It has been proposed [16] that the real and imaginary parts of QNMs in the eikonal limit have a compact connection to the angular velocity and Lyapunov exponent of unstable circular null geodesics. We adopt the geometric unit throughout this paper as usual

NULL GEODESICS

Q2 exp

CORRESPONDENCE BETWEEN QN

Findings

CONCLUSIONS