Shear-free perfect fluids with linear equation of state

TL;DR

This paper proves a conjecture about shear-free perfect fluid solutions in Einstein's equations, showing they are either expansion-free or non-rotating for most linear equations of state.

Contribution

It establishes a nearly complete proof of the Treciokas-Ellis conjecture for all but six specific values of the equation of state parameter w.

Findings

Shear-free perfect fluids are either expansion-free or non-rotating.

The proof applies to all linear equations of state except six specific values of w.

Most shear-free solutions conform to the conjecture, with exceptions only at six values of w.

Abstract

We prove that shear-free perfect fluid solutions of Einstein's field equations must be either expansion-free or non-rotating (as conjectured by Treciokas and Ellis) for all linear equations of state $p = w \rho$ except for six values of $w$.