Consistency of dust solutions with div H=0

TL;DR

This paper demonstrates that in irrotational dust spacetimes, the condition div H=0, crucial for gravitational radiation, remains consistent throughout the nonlinear evolution, extending previous linear analyses.

Contribution

It proves the nonlinear consistency of the div H=0 condition in irrotational dust spacetimes, advancing understanding of gravitational radiation conditions.

Findings

div H=0 condition is preserved in nonlinear evolution

Supports the role of div H=0 as a covariant gravitational radiation criterion

Extends previous linear results to exact nonlinear theory

Abstract

One of the necessary covariant conditions for gravitational radiation is the vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab} itself is nonzero. We complete a recent analysis by showing that in irrotational dust spacetimes, the condition div H=0 evolves consistently in the exact nonlinear theory.