Quasi-normal modes of near-extremal black holes and black strings in massive gravity background

Abstract

In this paper, two numerical methods are used to calculate quasi-normal modes (QNMs) of near-extremal black holes/strings in the generalized spherically/cylindrically symmetric background, the Asymptotic Iteration Method (AIM) and the Spectral Method. The numerical results confirm the accuracy of the approximate analytic formula using the Pöschl–Teller potential. Our analytic formula is used to investigate the Strong Cosmic Censorship conjecture of extremal and near-extremal black holes in (P. Burikham, S. Ponglertsakul and T. Wuthicharn, Eur. Phys. J. C 80 (2020) 954, arXiv:2010.05879 [gr-qc]).