Violations of the weak cosmic censorship conjecture in the higher dimensional $f(R)$ black holes with pressure

Abstract

We adopt the energy momentum relation of charged particles to study the thermodynamics laws and weak cosmic censorship conjecture of $D$-dimensional $f(R)$ AdS black holes in different phase spaces by considering charged particle absorption. In the normal phase space, it turns out that the laws of thermodynamic and the weak cosmic censorship conjecture are valid. In the extended phase space, though the first law of thermodynamics is valid, the second law of thermodynamics is invalid. More interestingly, the weak cosmic censorship conjecture is shown to be violated only in higher-dimensional near-extremal $f(R)$ AdS black holes. In addition, the magnitudes of the violations for both the second law and weak cosmic censorship conjecture are dependent on the charge $Q$, constant scalar curvature $f'(R_0)$, AdS radius $l$, dimension parameters $p$, and their variations.