Magnetic String Coupled to Nonlinear Electromagnetic Field

We introduce a class of rotating magnetically charged string solutions of the Einstein gravity with a nonlinear electrodynamics source in four dimensions. The present solutions has no curvature singularity and no horizons but has a conic singularity and yields a spacetime with a longitudinal magnetic field. Also, we investigate the effects of nonlinearity on the properties of the solutions and find that for the special range of the nonlinear parameter, the solutions are not asymptotic AdS. We show that when the rotation parameter is non zero, the spinning string has a net electric charge that is proportional to the magnitude of the rotation parameter. Finally, we use the counterterm method inspired by AdS/CFT correspondence and calculate the conserved quantities of the solutions.Comment: 13 pages, 3 figure

Wormhole solutions in the presence of nonlinear Maxwell field

Generalizing of the Maxwell field to nonlinear electrodynamics theories, we look for the magnetic solutions. In initial approximation these models give the usual linear electrodynamics. We consider a suitable metric and investigate the properties of the solutions. Also, we use the cut-and-paste method to construct wormhole structure. We generalize the static solutions to rotating spacetime and obtain conserved quantities.Comment: 15 pages, 7 figure

Slowly Rotating Black Holes in Einstein-Generalized Maxwell Gravity

In this paper, with considering the nonlinear electromagnetic field coupled to Einstein gravity, we obtain the higher dimensional slowly rotating charged black hole solutions. By use of the fact that the temperature of the extreme black hole is zero, we find that these solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons provide that the mass parameter $m$ is greater than an extremal value $m_{ext}$, an extreme black hole if $m=m_{ext}$ and a naked singularity otherwise. Also, we find that the asymptotic behavior of the spacetime is not anti deSitter for the special values of the nonlinearity parameter. Then, we compute the ADM mass, electrical charge, temperature, entropy, angular momentum and gyromagnetic ratio of the solutions. Calculations of the electromagnetic field, electrical charge, entropy and temperature showed that they are sensitive with respect to the changing of nonlinearity parameter.Comment: 12 page

Thermodynamic instability of topological black holes with nonlinear source

In this paper, we obtain higher dimensional topological black hole solutions of Einstein-$\Lambda$ gravity in the presence of a class of nonlinear electrodynamics. First, we calculate the conserved and thermodynamic quantities of ($n+1$)-dimensional asymptotically flat solutions and show that they satisfy the first law of thermodynamics. Also, we investigate the stability of these solutions in the (grand) canonical ensemble. Second, we endow a global rotation to the static Ricci-flat solutions and calculate the conserved quantities of solutions by using the counterterm method. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Then, we perform a stability analysis of the rotating solutions both in the canonical and the grand canonical ensembles.Comment: 17 pages with 14 figures, accepted in EPJ