The geometric optics approximation to a solution of Einstein's vacuum field equations is studied using the approach of Burnett [J. Math. Phys. 30, 90 (1989)] in which the usual averaging methods are replaced by the use of weak limits. The technique is applied to calculate the gravitational field of high-frequency gravity waves produced by isolated sources. The background space-time derived is of the Robinson-Trautman form with a nonvanishing Ricci tensor and the high-frequency, small-amplitude perturbation is explicitly calculated. In general, the wave fronts are homeomorphic to two-spheres. For purely spherical waves we exhibit the plane wave limit in the geometric optics approximation and thereby recover an example given by Burnett, but with two degrees of freedom of polarization present instead of his one. The identification of a mass-loss formula of the Bondi-Sachs type in the background space-time is also discussed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics