Overcharging problem and thermodynamics in extended phase spaces

Abstract

In this paper, the overcharging problem and thermodynamics in the extended phase spaces of the five-dimensional spherically symmetric topological black holes are investigated by absorptions of scalar particles and fermions. The cosmological constant is regarded as a variable related to pressure and its conjugate quantity is a thermodynamic volume. The first law of thermodynamics is recovered. The second law is violated in the extended phase space of the extremal and near-extremal black holes. The overcharging problem is tested by the existence of the event horizons. The event horizon is determined by the metric component f(r). The minimal values of the metric component at the final stage show that the extremal and near-extremal black holes can not be overcharged.