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

TL;DR

This paper derives higher-dimensional charged black hole solutions in Einstein gravity coupled with nonlinear electrodynamics, revealing diverse asymptotic behaviors and a critical exponent in odd dimensions affecting the metric's decay.

Contribution

It introduces a general class of solutions with a nonlinear electromagnetic source characterized by an arbitrary power of the Maxwell invariant, exploring their asymptotic properties and special critical cases.

Findings

Solutions resemble Reissner-Nordstrom black holes in certain ranges.

Existence of solutions with slower decay than Schwarzschild spacetime.

Identification of a critical exponent in odd dimensions causing logarithmic metric dependence.

Abstract

We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is deriving 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 resemble to the standard Reissner-Nordstrom 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 not asymptotically 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.