Homogeneous and hypersurfacehomogeneous shearfree perfect fluids ingeneral relativity.
Abstract
Shearfree, generalrelativistic perfect fluids are investigated in the case where they are either homogeneous or hypersurfacehomogeneous (and, in particular, spatially homogeneous). It is assumed that the energy density μ and the presurep of the fluid are related by a barotropic equation of statep = p(μ), where μ +p ≠ 0. Under such circumstances, it follows that either the fluid's volume expansion rate θ or the fluid's vorticity (i.e., rotation) ω must vanish. In the homogeneous case, this leads to only two possibilities: either ω = θ = 0 (the Einstein static solution), or ω ≠ 0,θ = 0 (the Gödel solution). In the hypersurfacehomogeneous case, the situation is more complicated: either ω = 0, θ≠ 0 (as exemplified,inter alia, by the FriedmannRobertsonWalker models), or ω ≠ 0, θ = 0 (which pertains, for example, in general stationary cylindrically symmetric fluids with rigid rotation, or ω = θ = 0 (as occurs for static spherically symmetric solutions). Each possibility is further subdivided in an invariant way, and related to the studies of other authors, thereby unifying and extending these earlier works.
 Publication:

General Relativity and Gravitation
 Pub Date:
 August 1988
 DOI:
 10.1007/BF00758905
 Bibcode:
 1988GReGr..20..847C
 Keywords:

 General Relativity:Relativistic Fluids;
 Relativistic Fluids:General Relativity