Shear-free perfect fluids with a solenoidal electric curvature

TL;DR

This paper proves that in shear-free perfect fluid solutions of Einstein's equations with a barotropic pressure and zero divergence of electric Weyl curvature, either vorticity or expansion must vanish.

Contribution

It establishes a new condition linking shear-free fluids, electric Weyl curvature, and fluid kinematics in general relativity.

Findings

Vorticity vanishes under specified conditions.

Expansion vanishes under specified conditions.

Electric Weyl curvature divergence condition is crucial.

Abstract

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.