Magnetic Branes in Third Order Lovelock-Born-Infeld Gravity

TL;DR

This paper introduces a new class of magnetic brane solutions in third order Lovelock-Born-Infeld gravity, revealing their geometric properties, effects of electromagnetic nonlinearity, and conserved quantities, with implications for higher-dimensional gravity theories.

Contribution

The paper presents novel magnetic brane solutions incorporating nonlinear electromagnetic fields in third order Lovelock gravity, analyzing their geometric features and conserved quantities.

Findings

Solutions have no curvature singularity or horizons.

Deficit angle increases as electromagnetic nonlinearity grows.

Conserved quantities are independent of the Born-Infeld parameter.

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.