A new black hole solution in dilaton gravity inspired by power-law electrodynamics

Abstract

In this work, a new class of slowly rotating black hole solutions in dilaton gravity has been obtained where dilaton field is coupled with nonlinear Maxwell invariant. The background space–time is a stationary axisymmetric geometry. Here, it has been shown that the dilaton potential can be written in the form of generalized three Liouville-type potentials. In the presence of these three Liouville-type dilaton potentials, the asymptotic behavior of the obtained solutions is neither flat nor (A)dS. One bizarre property of the electric field is that the electric field goes to zero when [Formula: see text] and diverges at [Formula: see text]. We show the validity of the first law of thermodynamics in thermodynamic investigations. The local and global thermodynamical stability are investigated through the use of heat capacity and Gibbs free energy. Also, the bounded, phase transition and the Hawking–Page phase transition points as well as the ranges of black hole stability have been shown in the corresponding diagrams. From these diagrams, we can say that the presence of the dilaton field makes the solutions to be locally stable near origin and vanishes the global stability of our solutions. In final thermodynamics analysis, we obtain the Smarr formula for our solution. We will show that the presence of dilaton field brings a new term in the Smarr formula. Also, we find that the dilaton field makes the black hole (AdS) mass to decrease for every fix values of [Formula: see text] (entropy).