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.

Electromagnetic waves in the Kerr–Schild metric

“…In order to describe the behaviour of this wave when entering a plane gravitational wave at an angle γ , the amplitude and polarisation are calculated by substituting (37) into (28) and (33), and then fed into (9) using (25) to give F. A given transverse profile in Minkowski space is generalised to gravitational wave space by replacing x and y with the basis functions X γ and Y γ . Thus, a circularly polarised Gaussian light beam with width parameter σ would be given by…”

“…However, one should remember that this represents an idealisation. In particular, the Bondi news function for this class of metrics has been found to be zero, suggesting that the Kerr-Schild metric cannot globally describe gravitational radiation from bounded sources [27,28]. 2 We will occasionally transform to an alternative co-ordinate chart to facilitate intermediate calculations but the results will ultimately be presented in the Kerr-Schild metric.…”