Scalar field quasinormal frequencies of Reissner-Nordstr\"om black hole surrounded by quintessence by using he continued fraction method

TL;DR

This paper calculates the quasinormal frequencies of a scalar field around a charged black hole in a quintessence field using the continued fraction method, revealing how quintessence affects oscillation and damping.

Contribution

It provides the first detailed analysis of scalar quasinormal modes of Reissner-Nordström black holes with quintessence using the continued fraction method for specific quintessence parameters.

Findings

Quintessence decreases oscillation frequencies for all angular modes.

Quintessence increases damping times for modes with angular momentum l>0.

The study derives Frobenius series solutions for special quintessence parameters.

Abstract

We evaluate the quasinormal modes of massless scalar field around Reissner-Nordstr$\ddot{\text{o}}$m black hole surrounded by a static and spherically symmetric quintessence by using the continued fraction method. The appropriate Frobenius series for three special cases of the quintessence parameter $ \epsilon = -1/3, -2/3$ and $-1$ are derived successfully. We show that the variation of quasinormal frequencies with charge of the black hole and the quintessential parameters. The numerical results show that quintessence field decreases oscillation frequencies of all angular momentum $l$ modes and increases the damping time of $l>0$ modes.