Contributions to the study of general relativistic shear-free perfect fluids: an approach involving Cartan's equivalence method, differential forms and symbolic computation
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Date
1993
Authors
Lang, Jérôme Michel
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Publisher
University of Waterloo
Abstract
It has been conjectured that general relativistic shear-free perfect fluids with a barotropic equation of state, and such that the energy density, µ, and the pressure, p, satisfy µ + p ̸= 0, cannot simultaneously be rotating and expanding (or contracting). A survey of the known results about this conjecture is included herein. We show that the conjecture holds true under either of the following supplementary conditions: 1) the Weyl tensor is purely magnetic with respect to the flow velocity vector or 2) dp/dµ = −1/3.
Any hypersurface-homogeneous shear-free perfect fluid which is not space-time homogeneous and whose acceleration vector is not parallel to the vorticity vector belongs to one of three invariantly defined classes, labelled A, B and C. It is found that the Petrov types which are allowed in each class are as follows: for class A, type I only; for class B, types I, II and III; and for class C, types I, D, II and N.
Two-dimensional pseudo-Riemannian space-times are classified in a manner similar to that of the Karlhede classification of four-dimensional general-relativistic space-times.
In an appendix, the forms differential forms package for the Maple program is described.
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Keywords
General Relativity, Cosmology, Equivalence Method, Shear-free conjecture, Differential forms Maple package