Quasi normal modes of a Casimir--like traversable wormhole through the semi-analytical WKB approach

TL;DR

This paper applies the semi-analytical WKB method to study scalar field quasi-normal modes in a Casimir-like traversable wormhole, revealing error estimates and quasi-resonance behavior similar to massive fields in black hole backgrounds.

Contribution

It introduces a semi-analytical WKB approach to compute quasi-normal modes in a Casimir-like wormhole, including error analysis and resonance phenomena.

Findings

Error in frequency computation varies with WKB order

Fundamental mode shows quasi-resonance behavior

Imaginary part of frequencies approaches zero for fundamental mode

Abstract

In this work, we implement the semi-analytical WKB method to explore the behaviour of a scalar field on a traversable wormhole space--time with a Casimir--like complexity reported in Eur. Phys. J. C 82, 420 (2022). We estimate the error in the computation of the quasi--normal frequencies of the scalar field at each order in the WKB and show that the order with the best accuracy is not unique. We compute the value of the quasinormal frequencies for the smallest estimated error. As an aside, we find that the imaginary part of the quasinormal modes frequencies approach to zero for the fundamental mode mimicking the so--called quasi--resonance observed for massive scalar fields in the Reissner--Nordstr\"{o}m background.