Abstract
A class of spinning magnetic string in 4-dimensional Einstein-dilaton gravity with Liouville type potential which produces a longitudinal nonlinear electromagnetic field is presented. These solutions have no curvature singularity and no horizon, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. Although the asymptotic behavior of these solutions are neither flat nor (A)dS, we calculate the conserved quantities of these solutions by using the counterterm method. We also generalize these four-dimensional solutions to the case of (n+1)-dimensional rotating solutions with k⩽[n/2] rotation parameters, and calculate the conserved quantities and electric charge of them.
Highlights
The Born-Infeld [1] type of generalizations of Abelian and non-Abelian gauge theories have received a lot of interest in recent years
The nonlinearity of the electromagnetic field brings remarkable properties to avoid the black hole singularity problem which may contradict the strong version of the Penrose cosmic censorship conjecture in some cases
The Born-Infeld action including a dilaton and an axion field, appears in the couplings of an open superstring and an Abelian gauge field. This action, describing a Born-Infeld-dilaton-axion system coupled to Einstein gravity, can be considered as a non-linear extension of the Abelian field of Einstein-Maxwell-dilaton-axion gravity
Summary
The Born-Infeld [1] type of generalizations of Abelian and non-Abelian gauge theories have received a lot of interest in recent years. AdS spacetimes generated by static and spinning magnetic sources in three and four dimensional Einstein-Maxwell gravity with negative cosmological constant have been investigated in [35, 36] The generalization of these rotating solutions to higher dimensions and higher derivative gravity have been done in [37] and [38], respectively. Exact magnetic rotating solutions in three dimensions have been considered in [43] while, two classes of magnetic rotating solutions in four and higher dimensional EMd gravity with Liouville-type potential have been explored in [44] and [45], respectively These solutions are not black holes, and represent spacetimes with conic singularities.
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