Twistors and linearized Einstein theory on plane-fronted impulsive wave backgrounds

The spinor form of linearized gravitation on a curved vacuum background is obtained from the Bianchi identities. There are no Buchdahl constraints to be satisfied, and for a flat background the approach reduces to the usual massless spin 2 theory. The equations are specialized to the plane-fronted impulsive gravitational wave backgrounds which include the ultrarelativistic limit of a moving black hole. Given a solution of the resulting system, it is possible to construct the metric perturbations up to gauge terms. It is shown that this linearized scheme is equivalent to the proposed twistor Hamiltonian formalism. As an example, colliding plane impulsive waves are considered, and the model compares well with the known exact solution. A discussion is given of the application of these methods to ultrarelativistic black-hole encounters. (author)