Quasinormal Modes of a Schwarzschild Black Hole Immersed in an Electromagnetic Universe

TL;DR

This paper analyzes the quasinormal modes of a Schwarzschild black hole immersed in an electromagnetic universe, using both analytical transformations to Heun's equations and numerical WKB methods to derive the QNMs.

Contribution

It introduces a novel approach to study QNMs of an immersed Schwarzschild black hole by transforming perturbation equations into confluent Heun's form and applying numerical techniques.

Findings

Analytical solutions via confluent Heun's equations.

Numerical QNM frequencies obtained with WKB method.

Discussion of QNM behavior in electromagnetic universe context.

Abstract

We study the quasinormal modes (QNMs) of the Schwarzschild black hole immersed in an electromagnetic (em) universe. The immersed Schwarzschild black hole (ISBH) is originated from the metric of colliding em waves with double polarization [Class. Quantum Grav. 12, 3013 (1995)]. The perturbation equations of the scalar fields for the ISBH geometry are written in the form of separable equations. We show that these equations can be transformed to the confluent Heun's equations, for which we are able to use the known techniques to perform the analytical quasinormal (QNM) analysis of the solutions. Furthermore, we employ numerical methods [Mashhoon and $6^{th}$-order Wentzel-Kramers-Brillouin (WKB)] to derive the QNMs. The results obtained are discussed and depicted with the appropriate plots.