Recent researches of the novel 4D Einstein–Gauss–Bonnet (EGB) gravity have attracted great attention. In this paper, we investigate the validity of the weak cosmic censorship conjecture for a novel 4D charged EGB black hole with test charged scalar field and test charged particle respectively. For the test charged field scattering process, we find that both extremal and near-extremal black holes cannot be overcharged. For the test charged particle injection, to first order, an extremal black hole cannot be overcharged while a near-extremal 4D charged EGB black hole can be destroyed. To second order, however, both extremal and near-extremal 4D charged EGB black holes can be overcharged for positive Gauss–Bonnet coupling constant; for negative Gauss–Bonnet coupling constant, an extremal black hole cannot be overcharged and the validity of the weak cosmic censorship conjecture for a near-extremal black hole depends on the Gauss–Bonnet coupling constant.

Motivated by the recent researches of black holes with NUT charge, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black hole with a test massive scalar field and a test particle, respectively. For the scalar field scattering gedanken experiment, we consider an infinitesimal time interval process. The result shows that both extremal and near-extremal Kerr-Taub-NUT black holes cannot be over-spun. For the test particle thought experiment, the study suggests that extremal Kerr-Taub-NUT black hole cannot be over-spun; while near-extremal Kerr-Taub-NUT black hole can be over-spun. By comparing the two methods, the results indicate the time interval for particles crossing the black hole horizon might be important for consideration of the weak cosmic censorship conjecture.

In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in f(R) gravity. We obtain several typical thick brane solutions for $$f(R)=R+\alpha R^2$$ f ( R ) = R + α R 2 . To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with $$df/dR>0$$ d f / d R > 0 is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter $$\alpha $$ α on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances.