Abstract
Considering the Einstein gravity in the presence of Born-Infeld type electromagnetic fields, we introduce a class of 4-dimensional static horizonless solutions which produce longitudinal magnetic fields. Although these solutions do not have any curvature singularity and horizon, there exists a conic singularity. We investigate the effects of nonlinear electromagnetic fields on the properties of the solutions and find that the asymptotic behavior of the solutions is adS. Next, we generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Furthermore, conserved quantities will be calculated through the use of the counterterm method. Finally, we extend four-dimensional magnetic solutions to higher dimensional solutions. We present higher dimensional rotating magnetic branes with maximum rotation parameters and obtain their conserved quantities.
Highlights
One of the interesting topological defects is cosmic string which may be originated during the early universe phase transitions [1]
Magnetic strings have been studied in Brans-Dicke theory as well as dilaton gravity [10,11,12,13]
In addition to Lorentz and U(1) gauge invariances, we know that the Lagrangian of the Maxwell electrodynamics contains only quadratic forms of gauge potential and its first derivative
Summary
One of the interesting topological defects is cosmic string which may be originated during the early universe phase transitions [1] (see Kibble mechanism for more details [2]). Interesting properties and interaction of the superconducting cosmic string with astrophysical magnetic fields have been found in [7,8,9]. In addition to Lorentz and U(1) gauge invariances, we know that the Lagrangian of the Maxwell electrodynamics contains only quadratic forms of gauge potential and its first derivative. One can consider both invariances and leave out the third condition to obtain NLED [60]. Considering the relation between AdS/CFT correspondence and superconductivity phenomenon, it was shown that the BI type theories make a crucial effect on the condensation, the critical temperature, and energy gap of the superconductors [87]. One of the elemental motivations for analyzing the horizonless string solutions is that they may be interpreted as cosmic strings
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