Contributions to the study of general relativistic shear-free perfect fluids: an approach involving Cartan's equivalence method, differential forms and symbolic computation

[摘要] 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.

[发布机构] University of Waterloo

[效力级别] Cosmology

[关键词] General Relativity;Equivalence Method;Differential forms Maple package;Cosmology;Shear-free conjecture;Doctoral Thesis