Comment on "Comment on linear confinement of a scalar particle in a G\"{o}del-type space-time"

TL;DR

This paper corrects the energy eigenvalues for the Klein-Gordon equation in Som-Raychaudhuri space-time with a cosmic string, clarifying previous inaccuracies by manipulating the biconfluent Heun differential equation.

Contribution

It provides a corrected derivation of the energy eigenvalues for a scalar particle in a specific curved space-time background, addressing errors in prior work.

Findings

Corrected energy eigenvalues for Klein-Gordon in Som-Raychaudhuri space-time

Demonstrated the proper use of biconfluent Heun equation in this context

Refuted previous incorrect results in the literature

Abstract

We show that from an appropriate manipulation of the biconfluent Heun differential equation can obtain the correct expression for the energy eigenvalues for the Klein-Gordon equation without potential in the background of Som-Raychaudhuri space-time with a cosmic string as a case particular ($k_{L}=0$) of [Vit\'{o}ria et al. Eur. Phys. J. C (2018) 78:44], in opposition what was stated in a recent paper published in this journal [F. Ahmed, Eur. Phys. J. C (2019) 79:682].