Shear-free perfect fluids with a barotropic equation of state in general relativity: the present status

TL;DR

This paper reviews the shear-free fluid conjecture in general relativity, provides a new complete proof for linear equations of state with cosmological constant, and discusses progress towards a general proof.

Contribution

It offers a comprehensive review, a new complete proof for linear equations of state, and useful results aiding the conjecture's proof for general cases.

Findings

Partial proofs of the conjecture are summarized.

A new complete proof is provided for linear equations of state.

Results may facilitate proving the conjecture for general equations of state.

Abstract

The present status of the shear-free fluid conjecture in general relativity is discussed: a review is given of recent partial proofs, a new and complete proof is given for the case of a linear equation of state, including a non-zero cosmological constant, and a number of useful results are presented which might help in proving the conjecture for a general equation of state.