Quasi-normal Modes of near-extremal black holes in Generalized spherically symmetric spacetime and Strong Cosmic Censorship Conjecture

TL;DR

This paper derives an analytic formula for quasinormal modes of near-extremal generalized spherically symmetric black holes and examines their implications for the Strong Cosmic Censorship conjecture, revealing violations in certain conditions.

Contribution

It provides the first analytic expression for quasinormal frequencies in this context and analyzes SCC violations in generalized black hole spacetimes.

Findings

Christodoulou SCC is violated in some parameter regions.

$C^{1}$ SCC remains valid universally.

Analytic quasinormal mode formula derived for near-extremal black holes.

Abstract

A number of near-extremal conditions are utilized to simplify the equation of motion of the neutral scalar perturbations in generalized spherically symmetric black hole background into a differential equation with the P\"{o}schl-Teller potential. An analytic formula for quasinormal frequencies is obtained. The analytic formula is then used to investigate Strong Cosmic Censorship conjectures~(SCC) of the generalized black hole spacetime for the smooth initial data. The Christodoulou version of the SCC is found to be violated for certain regions of the black hole parameter space including the black holes in General Relativity while the $C^{1}$ version of the SCC is always valid.