Shear-free perfect fluids with linear equation of state

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 Ellis and Treciokas) for all linear equations of state p = wρ except for w

Geometry of almost-product Lorentzian manifolds and relativistic observer

“…This suggests possible relationships between metric and fluid observer, which are an interesting subject for future research (see e.g. [18,22]).…”