Gravitational radiation, vorticity and the electric and magnetic part of Weyl tensor

TL;DR

This paper analyzes the electric and magnetic parts of the Weyl tensor in Bondi vacuum spacetimes, establishing conditions for staticity and Minkowski spacetime, and explores the connection between vorticity and gravitational radiation.

Contribution

It provides a detailed calculation of Weyl tensor invariants in Bondi spacetimes and links the electric part's behavior to staticity and Minkowski space, also discussing vorticity's relation to gravitational waves.

Findings

Electric part vanishes only in static spacetimes.

Magnetic part does not include static field contributions.

Vanishing electric part implies Minkowski spacetime.

Abstract

The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms of the Weyl tensor containing the static part of the field. It is shown that the necessary and sufficient condition for the spacetime to be purely electric is that such spacetime be static. It is also shown that the vanishing of the electric part implies Minkowski spacetime. Unlike the electric part, the magnetic part does not contain contributions from the static field. Finally a speculation about the link between the vorticity of world lines of observers at rest in a Bondi frame, and gravitational radiation, is presented.