Thermodynamics of charged A(dS) black holes with quadratically-extended electrodynamics

Abstract

In this paper, the Einstein-nonlinear electromagnetic theory has been studied in the four-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes. A new class of nonlinearly charged A(dS) black hole solution, in the presence of quadratically-extended Maxwell field, has been obtained and the thermodynamical properties have been analyzed. The black hole entropy, temperature and electric potential have been calculated, making use of the geometric methods. Through a Smarr mass formula the black hole mass has been written as a function of the complete set of extensive parameters (i.e. charge and entropy). It has been found that the intensive parameters (i.e. electric potential and temperature) obtained from the mass formula coincide with their values obtained from geometric approaches. It confirms the validity of the first law of black hole thermodynamics. A black hole stability analysis has been performed from the canonical ensemble approach, regarding the black hole heat capacity with the black hole charge as a constant. The points of type one and type two phase transitions, and the ranges at which the new charged A(dS) black holes are locally stable have been determined. Also, for the new charged black holes to be physically reasonable, their charge has been restricted to some specific ranges.