Abstract
We construct a new class of charged rotating black string solutions coupled to dilaton and exponential nonlinear electrodynamic fields with cylindrical or toroidal horizons in the presence of a Liouville-type potential for the dilaton field. Due to the presence of the dilaton field, the asymptotic behaviors of these solutions are neither flat nor (A)dS. We analyze the physical properties of the solutions in detail. We compute the conserved and thermodynamic quantities of the solutions and verify the first law of thermodynamics on the black string horizon. When the nonlinear parameterβ2goes to infinity, our results reduce to those of black string solutions in Einstein-Maxwell-dilaton gravity.
Highlights
The field equations of Einstein theory of general relativity have nonlinear nature
The second type of nonlinear Lagrangian which has the logarithmic (LN) form was introduced by Soleng [2], and recently the exponential nonlinear (EN) Lagrangian for the electrodynamics was suggested by Hendi [3,4,5] as the third type of nonlinear electrodynamics
We constructed a new class of four-dimensional rotating black string solutions with cylindrical or toroidal horizons coupled to EN electrodynamic and dilaton fields
Summary
The field equations of Einstein theory of general relativity have nonlinear nature When these field equations are coupled to the linear Maxwell field, they admit the wellknown charged static and spherically symmetric ReissnerNordstrom (RN) black hole solution. In the scalar-tensor theories of gravity, black holes solution coupled to BI nonlinear electrodynamics have been studied in [57, 58]. The studies were generalized to EN electrodynamics coupled to the dilaton field (ENd) In this regard, a new class of static and spherically symmetric solutions in four dimensional-ENd gravity was constructed in [59]. We would like to extend the study on ENd theory by constructing a new class of rotating dilaton black string solutions with cylindrical or toroidal horizons in the presence of EN electromagnetic field. We finish our paper with conclusions in the last section
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