# Strong Cosmic Censorship under Quasinormal Modes of Non-Minimally Coupled Massive Scalar Field

## TL;DR

This paper examines the validity of the strong cosmic censorship conjecture in specific black hole spacetimes by analyzing quasinormal modes of a non-minimally coupled massive scalar field, revealing conditions under which the conjecture holds.

## Contribution

It introduces a detailed analysis of quasinormal modes for non-minimally coupled massive scalar fields in lukewarm Reissner-Nordström-de Sitter and Martinez-Troncoso-Zanelli black holes, linking scalar field properties to cosmic censorship validity.

## Key findings

- Strong cosmic censorship holds except in small-mass black hole limit.
- Scalar field coupling and mass influence decay rates and censorship validity.
- Dominant quasinormal modes are connected via WKB approximation.

## Abstract

We investigate the strong cosmic censorship conjecture in lukewarm Reissner-Nordstr\"{o}m-de Sitter black holes (and Mart\'{i}nez-Troncoso-Zanelli black holes) using the quasinormal resonance of non-minimally coupled massive scalar field. The strong cosmic censorship conjecture is closely related to the stability of the Cauchy horizon governed by the decay rate of the dominant quasinormal mode. Here, dominant modes are obtained in the limits of small and large mass black holes. Then, we connect the modes by using the WKB approximation. In our analysis, the strong cosmic censorship conjecture is valid except in the range of the small-mass limit, in which the dominant mode can be assumed to be that of the de Sitter spacetime. Particularly, the coupling constant and mass of the scalar field determine the decay rate in the small mass range. Therefore, the validity of the strong cosmic censorship conjecture depends on the characteristics of the scalar field.