Higher-dimensional black holes with a conformally invariant Maxwell source

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 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. Since we are considering a power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression for the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordstr\om field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.