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Theorems on shear-free perfect fluids with their Newtonian analogues

J. M. M. Senovilla·C. F. Sopuerta·P. Szekeres
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Abstract

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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J. M. M. Senovilla, C. F. Sopuerta, P. Szekeres. 1997-02-18. Theorems on shear-free perfect fluids with their Newtonian analogues. https://doi.org/10.1023/a%3A1018854608416

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