Stability of Cauchy horizon in Einstein–Power–Maxwell–de Sitter black holes

Abstract

Abstract We investigated the Strong Cosmic Censorship (SCC) conjecture in Einstein–Power–Maxwell–de Sitter (EPMdS) black holes by analyzing the quasinormal modes (QNMs) of a massless neutral scalar field perturbation. Using the pseudospectral method, we calculated the QNM frequencies across various cosmological constants and nonlinear electromagnetic parameters. Our results show that for black holes far from extremality, the lowest QNM frequency $$-\text {Im} (\omega )/\kappa _-$$ - Im ( ω ) / κ - remains below 1/2. However, as the black holes approach extremality, the lowest mode’s $$-\text {Im} (\omega )/\kappa _-$$ - Im ( ω ) / κ - consistently exceeds 1/2, leading to a violation of SCC. Moreover, with a fixed cosmological constant, as the nonlinearity parameter $$\alpha $$ α increases, the interval of SCC violation under the charge extremality ratio narrows. Considering that $$k = 1/2 + 1/\alpha $$ k = 1 / 2 + 1 / α is inversely proportional to $$\alpha $$ α , our results indicate that increasing the order k of the non-linear electromagnetic field can effectively mitigate SCC violations.