Irrotational dust with Div H=0

TL;DR

This paper demonstrates that for irrotational dust, the condition div H=0 implies the magnetic part of the Weyl tensor H_{ab} must vanish, revealing a key geometric constraint.

Contribution

It establishes a new link between shear tensor diagonalization and the vanishing of the magnetic Weyl tensor in irrotational dust models.

Findings

div H=0 leads to H_{ab}=0 in irrotational dust

Shear tensor diagonalization is consistent only when H_{ab}=0

Provides geometric constraints for dust cosmological models

Abstract

For irrotational dust the shear tensor is consistently diagonalizable with its covariant time derivative: $\sigma_{ab}=0=\dot{\sigma}_{ab},\; a\neq b$, if and only if the divergence of the magnetic part of the Weyl tensor vanishes: $div~H = 0$. We show here that in that case, the consistency of the Ricci constraints requires that the magnetic part of the Weyl tensor itself vanishes: $H_{ab}=0$.