The Projective Geometry of Simple Cosmological Models

Details The Projective Geometry of Simple Cosmological Models The Projective Geometry of Simple Cosmological Models

Feb 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985rspsa.397..233h&link_type=abstract

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 397, Issue 1813, pp. 233-243

Physics

3

Scientific paper

The conformal properties of flat space-time can be described in terms of the projective geometry of a four-dimensional quadric hypersurface, Ω, embedded in projective 5-space, P^5. In this paper it is shown how an arbitrary conformally flat metric can be defined by the selection of a single scalar field on Ω. The curvature tensor associated with this metric can then be calculated. The procedure is illustrated with a self-contained treatment of the geometry of Friedmann-Robertson-Walker models within the P^5 framework. The essential properties of these space-times, such as the location of conformal infinity, curvature singularities and matter flow lines, etc., are all incorporated in geometric diagrams that arise naturally from the projective geometric construction.

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