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.

Historical review added. Accepted by J. Math. Phys

References in corpus (2)

• Conformally flat FRW metrics
• Cosmological test of the Yilmaz theory of gravity

Cited by in corpus (17)

• FRW Universe Models in Conformally Flat Spacetime Coordinates. I: General Formalism
• Post-Newtonian Celestial Dynamics in Cosmology: Field Equations
• Gravitational orbits in the expanding universe revisited
• FRW Universe Models in Conformally Flat Spacetime Coordinates. II: Universe models with negative and vanishing spatial curvature
• Cosmology in Minkowski space
• Dynamic Field Theory and Equations of Motion in Cosmology
• Local gravitational physics of the Hubble expansion
• FRW Universe Models in Conformally Flat Spacetime Coordinates. III: Universe models with positive spatial curvature
• Early universe in quantum gravity
• Critical Cosmology in Higher Order Gravity
• Time dilation observed in Type Ia supernova light curves and its cosmological consequences
• Testing quantum gravity with primordial gravitational waves
• FLRW spaces as submanifolds of ${\mathbb{R}}^6$: restriction to the Klein-Gordon operator
• On The Equivalence of the FRW Field Equations and those of Newtonian Cosmology
• Lorentzian correction for the evolution of the CMB temperature
• On FLRW reductions of N=1 supergravity
• FLRW embeddings in ${\mathbb{R}}^{n+2}$, differential geometry and conformal photon propagator