Higher-dimensional black holes with a conformally invariant Maxwell source

TL;DR

This paper introduces a conformally invariant Maxwell action in higher dimensions, deriving electrically charged black hole solutions that generalize the Reissner-Nordstrom black hole to dimensions that are multiples of four.

Contribution

It presents a new conformally invariant Maxwell action in higher dimensions and derives exact black hole solutions with a purely radial electric field.

Findings

Black hole solutions exist only in dimensions multiple of four.

Electric field expression matches four-dimensional Reissner-Nordstrom field.

Mass and charge are explicitly identified using Hamiltonian formalism.

Abstract

We consider an action for an abelian gauge field for which the density is given by a power of the Maxwell Lagrangian. In d spacetime dimensions this action is shown to enjoy the conformal invariance if the power is chosen as d/4. We take advantage of this conformal invariance to derive black hole solutions electrically charged with a purely radial electric field. Because of considering power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression of the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordstrom field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.