Nonlinearly charged three-dimensional black holes in the Einstein-dilaton gravity theory

Abstract

In this article, the new black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory have been investigated in a three-dimensional space time. The coupled scalar, electromagnetic and gravitational field equations have been solved in a spherically symmetric geometry and it has been shown that the dilatonic potential, as the solution to the scalar field equation, can be written in the form of a generalized Liouville potential. Also, two new classes of charged dilatonic BTZ black hole solutions, in the presence of power-law nonlinear electrodynamics, have been constructed out which are asymptotically non-flat and non-AdS. The conserved and thermodynamic quantities have been calculated from geometrical and thermodynamical approaches, separately. The consistency of the results of these two alternative approaches confirms the validity of the first law of black hole thermodynamics for both of the new black hole solutions. The black holes stability or phase transitions have been studied, making use of the canonical ensemble method. The points of type one and type two phase transitions as well as the ranges at which the black holes are stable have been indicated by considering the heat capacity of the new black hole solutions.