Article

# Magnetic Branes in Third Order Lovelock-Born-Infeld Gravity

07/2008;
Source: arXiv

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.

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##### Article:Holographic Lovelock Gravities and Black Holes
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ABSTRACT: We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition for asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock gravity in seven spacetime dimensions we compute the holographic Weyl anomaly and determine the three point functions of the stress energy tensor in the boundary CFT. Remarkably, these correlators happen to satisfy the same relation as the one imposed by supersymmetry. We then compute the energy flux; requiring it to be positive is shown to be completely equivalent to requiring causality of the finite temperature CFT dual to the black hole. These constraints are not stringent enough to place any positive lower bound on the value of viscosity. Finally, we conjecture an expression for the energy flux valid for any Lovelock theory in arbitrary dimensions. Comment: 31 pages, 1 figure, harvmac, references added, calculation of viscosity/entropy ratio included
12/2009;

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### Keywords

$(n+1)$-dimensional magnetic brane solutions

Born-Infeld parameter

Born-Infeld parameter decreases

conserved quantities

counterterm method

curvature singularity

deficit angle increases

electromagnetic field

electromagnetic fields

gravity action

longitudinal nonlinear magnetic field

Lovelock coefficients

magnetic solutions

new class

nonlinear invariant terms

Riemann tensor

rotation parameters

static source

third order Lovelock gravity

third order Lovelock-Born-Infeld gravity