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

By M. Hassaïne, Cristián Martínez. 2008

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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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d2cdb1599c7c08150957489447228277e3f25e2