Perturbations in the Kerr-Newman dilatonic black hole background: Maxwell waves, the dilaton background, and gravitational lensing

Abstract

In this paper we continue the analysis of one of our previous papers and study the affect of the existence of a non-trivial dilaton background on the propagation of electromagnetic waves in the Kerr-Newman dilatonic black hole space-time. For this purpose we again employ the double expansion in both the background electric charge and the wave parameters of the relevant quantities in the Newman-Penrose formalism and then identify the first order at which the dilaton background enters Maxwell equations. We then assume that gravitational and dilatonic waves are negligible (at that order in the charge parameter) with respect to electromagnetic waves and argue that this condition is consistent with the solutions already found in the previous paper. Explicit expressions are given for the asymptotic behavior of scattered waves, and a simple physical model is proposed in order to test the effects. An expression for the relative intensity is obtained for Reissner-Nordstr\"om dilaton black holes using geometrical optics. A comparison with the approximation of geometrical optics for Kerr-Newman dilaton black holes shows that at the order to which the calculations are carried out gravitational lensing of optical images cannot probe the dilaton background.