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On the Structure of Conformal Singularities in Classical General Relativity. II Evolution Equations and a Conjecture of K. P. Tod

Richard P. A. C. Newman
Proceedings: Mathematical and Physical Sciences
Vol. 443, No. 1919 (Dec. 8, 1993), pp. 493-515
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52416
Page Count: 23
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Structure of Conformal Singularities in Classical General Relativity. II Evolution Equations and a Conjecture of K. P. Tod
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Abstract

Consideration is given to the Cauchy problem for perfect fluid space-times which evolve from an initial singularity of conformal type. The evolution equations for the conformally transformed, unphysical geometry are shown to be expressible as a first order symmetric hyperbolic system, albeit with a singular forcing term. It is concluded that the 3-metric on the initial hypersurface of the unphysical space-time constitutes the freely specifiable initial data. Subject to Penroses's Weyl Curvature Hypothesis, according to which the Weyl tensor was initially zero, it follows that the physical space-time is Robertson-Walker. This may provide a basis for a new explanation for the large-scale isotropy of the universe.

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