Expanding perfect fluid generalizations of the C-metric

TL;DR

This paper revisits perfect fluid solutions of the C-metric, revealing new expanding anisotropic models with potential cosmological applications and providing criteria for shearfree normality and staticity in Petrov type D spacetimes.

Contribution

It introduces a broader class of anisotropic perfect fluid solutions with non-zero expansion, extending previous vacuum solutions and offering new testable criteria for Petrov type D spacetimes.

Findings

Anisotropic perfect fluid spacetimes can have non-zero expansion.

Constructed explicit line elements for these models.

Provided criteria for shearfree normality and staticity.

Abstract

We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike non-shearing and non-rotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum C-metric as a limit case, can have \emph{non-zero} expansion, contrary to the conclusion in the original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type $D$ spacetimes in general, which we add in an appendix.