Boosted Kerr–Newman black holes

Abstract

Abstract In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr–Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr–Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson–Trautman coordinates to Bondi–Sachs, including the perturbation term of the boosted Robinson–Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy–momentum tensor the boosted Kerr–Newman solution. To this end, we consider the electromagnetic energy–momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy–momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr–Newman metric. To proceed, we examine the causal structure of the boosted Kerr–Newman black hole in Bondi–Sachs coordinates as in a preferred timelike foliation. We show that the ultimate effect of a nonvanishing charge is to shrink the overall size of the event horizon and ergosphere areas when compared to the neutral boosted Kerr black holes. Considering the preferred timelike foliation we obtain the electromagnetic fields for a proper nonrotating frame of reference. We show that while the electric field displays a pure radial behavior, the magnetic counterpart develops an involved structure with two intense lobes of the magnetic field observed in the direction opposite to the boost.