It has been conjectured that shear-free perfect fluids in general relativity, with an equation of state p=p(μ) and satisfying μ+p≠0, necessarily have either zero expansion or zero vorticity. We prove that this result holds in the restricted case when the fluid’s vorticity and acceleration are parallel. Specifically, we prove that if the vorticity is nonzero, the fluid’s volume expansion must vanish.

No abstract

We continue our previous investigation of shear-free perfect fluids in general relativity, under the assumptions that the fluid satisfies an equation of state p=p(μ) with μ+p≠0, and that the vorticity and acceleration of the fluid are parallel (and possibly zero). We classify algebraically the set of such solutions into thirteen invariant nonempty cases. In each case, we investigate the allowed isometry groups and Petrov types, and invariantly characterize the special subcases that arise. We also show how the various subcases are related to each other and to the works of previous authors.

No abstract

No abstract