Radiation and Boundary Conditions in the Theory of Gravitation

TL;DR

This paper demonstrates that Sommerfeld boundary conditions in weak gravitational fields imply the null nature of the curvature tensor's 1/r part and confirm energy flux via gravitational waves.

Contribution

It establishes a link between boundary conditions and the Petrov type of curvature, clarifying energy transfer in gravitational wave emission.

Findings

The 1/r curvature component is of Petrov type null.

Outgoing gravitational waves carry energy flux.

Boundary conditions determine the curvature's Petrov classification.

Abstract

The Sommerfeld boundary conditions, applied to an asymptotically weak gravitational field, are shown to imply that the 1/r part of the curvature tensor of a space-time, satisfying the Einstein equations, is of type null in the Petrov classification and that there is then a flux of energy carried away by the outgoing gravitational wave.