Kerr–Schild metrics and gravitational radiation

Abstract

We describe conditions assuring that the Kerr–Schild type solutions of Einstein's equations with pure radiation fields are asymptotically flat at future null infinity. Such metrics cannot describe “true” gravitational radiation from bounded sources—it is shown that the Bondi news function vanishes identically. We obtain formulae for the total energy and angular momentum at ℐ. As an example we consider a non-stationary generalization of the Kerr metric given by Vaidya and Patel. Angular momentum and total energy are expressed in closed form as functions of retarded time.