Theorems on shear-free perfect fluids with their Newtonian analogues

Details Theorems on shear-free perfect fluids with their Newtonian analogues Theorems on shear-free perfect fluids with their Newtonian analogues

1997-02-18

arxiv.org/abs/gr-qc/9702035v1

Gen.Rel.Grav.30:389-411,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, LaTeX. Submitted to GRG

Scientific paper

10.1023/A:1018854608416

In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.

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