A Survey of Strong Cosmic Censorship Conjecture Beyond Einstein's Gravity

TL;DR

This survey examines the strong cosmic censorship conjecture beyond Einstein's gravity, analyzing how modifications like $f(R)$ and Energy-Momentum Squared Gravities influence black hole stability and the decay of perturbations.

Contribution

It investigates the impact of additional parameters from modified gravity theories on the validity of the strong cosmic censorship conjecture in charged-de Sitter black holes.

Findings

Model parameters can control decay rates of quasi-normal modes.

Certain parameter ranges restore the stability needed for SCCC.

Numerical analysis supports the role of modified gravity in preserving determinism.

Abstract

The strong cosmic censorship conjecture (SCCC) proposed by Penrose states that the presence of the inner Cauchy horizon ($\mathcal{CH}$) in the black hole solutions does not threaten the deterministic nature of general relativity since it is actually unstable against the remnant perturbation fields that fall into the black hole. Although this conjecture is well-established for the asymptotically flat spacetimes in general relativity, it is challenged upon taking a small positive cosmological constant as required by observational data. This challenge can be fixed by finding even one type of quasi-normal mode whose decay rate is slow enough insofar as the remnant of perturbation is able to destroy the $\mathcal{CH}$. By aiming to investigate the role of the additional parameter induced by modified gravity in this scenario, we consider the charged-de Sitter black hole solutions of Einstein-Maxwell theory extended with $f(R)$ and Energy-Momentum Squared Gravities. Employing the numerical analysis of the deterministic criterion, we show that the presence of the model parameter of theories at hand within a given range controls the decay rate of the photon sphere quasi-normal modes (in the eikonal limit) to rescue SCCC.