On the Conformal forms of the Robertson-Walker metric

Abstract

All possible transformations from the Robertson-Walker metric to those conformal to the Lorentz-Minkowski form are derived. It is demonstrated that the commonly known family of transformations and associated conformal factors are not exhaustive and that there exists another relatively less well known family of transformations with a different conformal factor in the particular case that K = -1. Simplified conformal factors are derived for the special case of maximally-symmetric spacetimes. The full set of all possible cosmologically-compatible conformal forms is presented as a comprehensive table. A product of the analysis is the determination of the set-theoretical relationships between the maximally symmetric spacetimes, the Robertson-Walker spacetimes, and functionally more general spacetimes. The analysis is preceded by a short historical review of the application of conformal metrics to Cosmology.

arXiv commentHistorical review added. Accepted by J. Math. Phys

References in corpus (6)

• Closed Universes, de Sitter Space and Inflation
• The Conformal Group SO(4,2) and Robertson-Walker Spacetimes
• Conformally flat FRW metrics
• Cosmological test of the Yilmaz theory of gravity
• Stationary generalized Kerr-Schild spacetimes
• Kinematic cosmology in conformally flat spacetime

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