Repeatable light paths in the shearfree normal cosmological models

Abstract

Conditions for the existence of repeatable light paths (RLPs) in the shearfree normal cosmological models are investigated. It is found that in the conformally nonflat models the only RLPs are radial null geodesics (in the spherical case) and their analogues in the plane- and hyperbolically symmetric cases. In the conformally flat Stephani models, there exist special spherically-, plane- and hyperbolically symmetric subcases, in which all null geodesics are RLPs. They are slightly more general than the Friedmann -- Lema\^ıtre -- Robertson -- Walker (FLRW) models of the corresponding symmetries: their curvature index function $k(t)$ and the scale factor $R(t)$ are expressed through a single function of time. In addition to that, there exist special cases of the Stephani solution in which some of the null geodesics are RLPs. All these special cases are identified.

20 pages, no figures. This version matches the text published in PRD (except for some graphical conveniences that PRD does not accept). The PRD referee forced some useful information to be deleted to save space. The earlier version will be easier to use for calculations

References in corpus (2)

• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• The newest release of the Ortocartan set of programs for algebraic calculations in relativity

Cited by in corpus (7)

• Geometric optics in general relativity using bilocal operators
• Optical drift effects in general relativity
• Redshift drift in axially symmetric quasi-spherical Szekeres models
• Accelerating expansion or inhomogeneity? A comparison of the $\Lambda$CDM and Lema\^ıtre - Tolman models
• Exact inhomogeneous models and the drift of light rays induced by nonsymmetric flow of the cosmic medium
• Repeatable light paths in the conformally flat cosmological models
• Spectral Distortion in a Radially Inhomogeneous Cosmology