Higher-dimensional charged black hole solutions with a nonlinear electrodynamics source

We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is derived from a Lagrangian given by an arbitrary power of the Maxwell invariant. The form of the general solution suggests a natural partition for the different ranges of this power. For a particular range, we exhibit a class of solutions whose behavior resembles the standard Reissner-Nordström black holes. There also exists a range for which the black hole solutions approach asymptotically the Minkowski spacetime slower than the Schwarzschild spacetime. We have also found a family of non-asymptotical flat black hole solutions with an asymptotic behavior growing slower than the Schwarzschild-(anti)-de Sitter spacetime. In odd dimensions, there exists a critical value of the exponent for which the metric involves a logarithmic dependence. This critical value corresponds to the transition between the standard behavior and the solution decaying to Minkowski slower than the Schwarzschild spacetime.