Stability of Cauchy horizon in charged black holes surrounded by quintessential dark energy

By investigating the Quasinormal Modes of a massless neutral scalar field, we have explored the influence of dark energy on the strong cosmic censorship (SCC) of charged de Sitter-like black holes. The results indicate that SCC can consistently be violated as long as the black hole approaches extremality. However, as the state parameter sigma = 3 omega f + 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma = 3\omega _f + 1$$\end{document} of the dark energy increases and approaches zero, the width of SCC violation interval demonstrates an overall decreasing trend, converging towards zero. Specifically, our research has identified a critical state parameter sigma crt \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{\text {crt}}$$\end{document} for dark matter. Beyond this critical value, enhancing the state parameter effectively mitigates SCC violations. However, at this critical threshold, the width of the violation interval stabilizes or marginally increase. These findings reveal a nuanced relationship between the asymptotic properties of black holes and the validity of the SCC, offering profound insights into potential mechanisms governing both the occurrence and alleviation of SCC violations.