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

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.