Thermodynamics and weak cosmic censorship conjecture in Reissner-Nordström anti-de Sitter black holes with scalar field

Abstract

The thermodynamics and weak cosmic censorship conjecture in Reissner-Nordström anti-de Sitter black holes are investigated by the scattering of the scalar field. The first law of thermodynamics in the non-extremal Reissner-Nordström anti-de Sitter black hole is recovered by the scattering. The increase of the horizon radius indicates that the singularity is not naked in this black hole. For the near-extremal and extremal black holes, the validity is tested by the minimum values of the function f at their final states. It is found that both of the near-extremal and extremal black holes can not be overcharged. When ω=qϕ, the final state of the extremal black hole is still an extremal black hole. When ω≠qϕ, it becomes a near-extremal black hole with new mass and charge.