Quasinormal modes and the correspondence with shadow in black holes with a deficit solid angle and quintessence-like matter

TL;DR

This paper explores how the photon sphere, shadow radius, and quasinormal modes of a black hole are affected by a deficit solid angle and quintessence-like matter, confirming a correspondence between quasinormal modes and shadow in such spacetimes.

Contribution

It introduces a detailed analysis of quasinormal modes and shadow radius in black holes with deficit solid angles and quintessence-like matter, demonstrating their interrelation.

Findings

Photon sphere and shadow radius decrease with lower deficit angle and matter density.

Quasinormal mode frequencies increase as deficit angle and matter density decrease.

Strong agreement between quasinormal modes obtained via WKB approximation and shadow-based methods.

Abstract

In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a $4$-dimensional black hole with a deficit solid angle and quintessence-like matter. We find that the radii of the photon sphere and shadow decrease with the decreases of the deficit solid angle and density of quintessence-like matter. The quasinormal modes are gotten by the sixth order WKB approximation method and shadow radius, respectively. The values of the real part and imaginary parts of the quasinormal modes increase with the decrease of the values of the deficit solid angle and density of quintessence-like matter when the multipole number is fixed. The quasinormal modes gotten by these two methods are in good agreement, especially when the multipole number is large. It shows the correspondence between the quasinormal modes in the eikonal limit and shadow.