A New Black Hole Solution In Dilaton Gravity Inspired By Power-Law Electrodynamics

TL;DR

This paper introduces a new class of slowly rotating black hole solutions in dilaton gravity coupled with nonlinear electrodynamics, analyzing their thermodynamics, stability, and unique properties influenced by the dilaton field.

Contribution

It presents novel black hole solutions with generalized Liouville-type dilaton potentials and explores their thermodynamic behavior and stability characteristics.

Findings

Electric field vanishes at the origin and diverges at infinity.

Dilaton field affects the stability and phase transition points.

The Smarr formula includes a new term due to the dilaton field.

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 this three Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions are neither flat nor (A)dS. One bizarre property of the electric field is that the electric field goes to zero when $r\rightarrow 0$ and diverges at $r\rightarrow\infty$. 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 S(entropy).