Kerr--Schild metrics and gravitational radiation

TL;DR

This paper investigates Kerr--Schild solutions with pure radiation, showing they cannot describe true gravitational radiation, and derives formulas for energy and angular momentum at null infinity, including a non-stationary Kerr generalization.

Contribution

It establishes conditions for asymptotic flatness of Kerr--Schild solutions with pure radiation and provides explicit formulas for energy and angular momentum at null infinity.

Findings

Bondi news function vanishes for these solutions

Formulas for total energy and angular momentum at scri+

Non-stationary Kerr generalization with explicit functions of retarded time

Abstract

We describe conditions assuring that the Kerr--Schild type solutions of Einstein 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 scri+. As an example we consider 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.