Magnetic Branes in Third Order Lovelock-Born-Infeld Gravity

Abstract

Considering both the nonlinear invariant terms constructed by the electromagnetic field and the Riemann tensor in gravity action, we obtain a new class of $(n+1)$-dimensional magnetic brane solutions in third order Lovelock-Born-Infeld gravity. This class of solutions yields a spacetime with a longitudinal nonlinear magnetic field generated by a static source. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle $\delta$. We find that, as the Born-Infeld parameter decreases, which is a measure of the increase of the nonlinearity of the electromagnetic field, the deficit angle increases. We generalize this class of solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. We found that the conserved quantities do not depend on the Born-Infeld parameter, which is evident from the fact that the effects of the nonlinearity of the electromagnetic fields on the boundary at infinity are wiped away. We also find that the properties of our solution, such as deficit angle, are independent of Lovelock coefficients.

15 pages, one figure, references added, a subsection added

References in corpus (8)

• Topological Black Holes in Lovelock-Born-Infeld Gravity
• Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock Gravity and the Counterterm Method
• Thermodynamics of Rotating Black Branes in Gauss-Bonnet-Born-Infeld Gravity
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• Taub-NUT Black Holes in Third order Lovelock Gravity
• Thermodynamics of Rotating Solutions in Gauss-Bonnet-Maxwell Gravity and the Counterterm Method
• Magnetic Strings in Einstein-Born-Infeld-Dilaton Gravity
• Spacetimes with Longitudinal and Angular Magnetic Fields in Third Order Lovelock Gravity

Cited by in corpus (4)

• Rotating Black Branes in the presence of nonlinear electromagnetic field
• A note on differences between (4+1)- and (5+1)-dimensional anisotropic cosmology in the presence of the Gauss-Bonnet term
• Solution for Static, Spherically Symmetric Lovelock Gravity Coupled with Yang-Mills Hierarchy
• Domain walls in Born-Infeld-dilaton background