Repeatable light paths in the conformally flat cosmological models

Abstract

This is a supplement to an earlier paper (PRD 84, 023510 (2011)), where those shearfree normal cosmological models were identified, in which all light rays have repeatable paths. All of them are conformally flat, but less general than the Stephani model and more general than Robertson --Walker. In this note, their defining feature is identified: in each of them, in comoving coordinates, the time-dependence factors out so that the cofactor is a static metric. Some related properties of conformal transformations are briefly discussed. Using an explicit example, it is shown that, with a suitably defined congruence of test observers and sources, non-repeatable light paths exist even in the Minkowski spacetime.

3 pages, no figures. This replacement matches the published version. Shortened from 5 pages by condensing the prose and deleting details of calculation in the appendix. Journal reference added

References in corpus (3)

• Cosmic Parallax: possibility of detecting anisotropic expansion of the universe by very accurate astrometry measurements
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• Repeatable light paths in the shearfree normal cosmological models

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• Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium
• Redshift drift in a universe with structure II: Light rays propagated through a Newtonian N-body simulation