General boosted black holes: a first approximation

Abstract

In this paper we obtain an approximate solution of Einstein field equations which describes a general boosted Kerr–Newman black hole relative to a Lorentz frame at future null infinity. The boosted black hole is obtained from a general twisting metric whose boost emerges from the Bondi–Metzner–Sachs group. Employing a standard procedure we build the electromagnetic energy-momentum tensor with the Kerr boosted metric together with its timelike killing vector as the electromagnetic potential. We demonstrate that our solution satisfies Einstein field equations up to a fourth-order expansion in 1/r, indicating that the spacetime closely resembles a Kerr–Newman black hole whose boost points in a arbitrary direction. Spacetime structures of the general black hole—namely the event horizon and ergosphere—are examined in Bondi–Sachs coordinates. For a proper timelike observer we show that the electric field generated by the boosted black hole exhibits a purely radial behavior, whereas the magnetic field develops a complex structure characterized by two pronounced lobes oriented opposite to the boost direction.