Slowly Rotating Black Holes in Einstein-Generalized Maxwell Gravity

Abstract: In this paper, with considering the nonlinear electromagnetic field coupled to Einstein gravity, we obtain the higher dimensional slowly rotating charged black hole solutions. By use of the fact that the temperature of the extreme black hole is zero, we find that these solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons provide that the mass parameter $m$ is greater than an extremal value $m_{ext}$, an extreme black hole if $m=m_{ext}$ and a naked singularity otherwise. Also, we find that the asymptotic behavior of the spacetime is not anti deSitter for the special values of the nonlinearity parameter. Then, we compute the ADM mass, electrical charge, temperature, entropy, angular momentum and gyromagnetic ratio of the solutions. Calculations of the electromagnetic field, electrical charge, entropy and temperature showed that they are sensitive with respect to the changing of nonlinearity parameter.