Thermodynamic properties of dilaton black holes with nonlinear electrodynamics

We examine the (n + 1)-dimensional (n ≥ 3) action in which gravity is coupled to the Born–Infeld nonlinear electrodynamic and a dilaton field. We construct a new (n + 1)-dimensional analytic solution of this theory in the presence of Liouville-type dilaton potentials. These solutions, which describe charged topological dilaton black holes with nonlinear electrodynamics, have unusual asymptotics. They are neither asymptotically flat nor (anti)-de Sitter. The event horizons of these black holes can be an (n - 1)-dimensional positive, zero or negative constant curvature hypersurface. We also analyze the thermodynamics and stability of these solutions and disclose the effect of the dilaton and Born–Infeld fields on the thermal stability in the canonical ensemble.

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Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

International Journal of Modern Physics D ◽

10.1142/s021827181850075x ◽

2018 ◽

Vol 27 (07) ◽

pp. 1850075 ◽

Cited By ~ 5

Author(s):

S. Hajkhalili ◽

A. Sheykhi

Keyword(s):

Black Holes ◽

Electric Field ◽

Gauge Field ◽

Causal Structure ◽

Nonlinear Electrodynamics ◽

Thermodynamic Quantities ◽

Dilaton Field ◽

Maximum Value ◽

Nonlinear Gauge ◽

Dilaton Black Holes

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born–Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein–Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as [Formula: see text]. The maximum value of the electric field increases with increasing the nonlinear parameter [Formula: see text] or decreasing the dilaton coupling [Formula: see text] and is shifted to the singularity in the absence of either dilaton field ([Formula: see text]) or nonlinear gauge field ([Formula: see text]).

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