Shear-free perfect fluids with a barotropic equation of state in general relativity: an update and a new formalism

Abstract

The present status of the shear-free perfect fluid conjecture in general relativity is discussed: I give a review of recent work and present a new formalism which may provide a better understanding of the problems encountered.

27 pages; added a section on coordinates, added extra references and removed a number of typo's. arXiv admin note: text overlap with arXiv:1510.05798; added explanations; added a short proof of the parallel case; added a short proof of the case where matter density and expansion are functionally related