# Charged Particle and Strong Cosmic Censorship in Reissner-Nordstr\"{o}m-de Sitter Black Holes

## TL;DR

This paper examines the instability of charged null particles in near-extremal Reissner-Nordström-de Sitter black holes and demonstrates that the strong cosmic censorship conjecture holds under these conditions by analyzing quasinormal modes.

## Contribution

It establishes a connection between unstable circular orbits of charged particles and quasinormal modes, providing evidence for the validity of the strong cosmic censorship conjecture in near-extremal black holes.

## Key findings

- Instability depends on black hole mass and charge.
- Charged null particles relate to scalar field quasinormal modes.
- Strong cosmic censorship is upheld in near Nariai-type extremal conditions.

## Abstract

We investigate the instability of the unstable circular orbit of a charged null particle to test the strong cosmic censorship conjecture in Nariai-type near-extremal Reissner--Nordstr\"{o}m--de Sitter black holes. The instability is estimated as the Lyapunov exponent and found to depend on the mass and charge of the black hole. Then, we explicitly show that charged null particles in unstable circular orbits correspond to the charged massless scalar field in the eikonal limit. This provides a compact relationship representing the quasinormal frequency in terms of the characteristics of unstable circular orbits in near Nariai-type extremal conditions. According to this relationship, the strong cosmic censorship conjecture is valid.