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

General Relativity;Cosmology;Equivalence Method;Shear-free conjecture;Differential forms Maple package

Lang, Jérôme Micheladvisor:Collins, Christopher Barry ; affiliation1:Faculty of Mathematics ; Collins, Christopher Barry ;

University of Waterloo

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

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/13075/1/Lang_Jerome_Michel_PhD_thesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 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.