Shear free barotropic perfect fluids cannot rotate and expand simultaneously

TL;DR

This paper proves a longstanding conjecture in general relativity that shear-free barotropic perfect fluids cannot simultaneously rotate and expand, establishing a fundamental restriction on their motion.

Contribution

It provides a rigorous proof that shear-free barotropic perfect fluids in general relativity cannot exhibit both rotation and expansion at the same time.

Findings

Shear-free condition implies either zero rotation or zero expansion.

Confirms a long-standing conjecture in the field.

Enhances understanding of fluid dynamics in relativistic contexts.

Abstract

We prove here a long standing conjecture in general relativity, that if barotropic perfect fluid is moving in a shear free way, then it must be either expansion free or rotation free.