On the structure of conformal singularities in classical general relativity. II: Evolution equations and a conjecture of K. P. Tod. (English) Zbl 0810.53086
Summary: [Part I, see the review above, Zbl 0810.53086.]
Consideration is given to the Cauchy problem for perfect fluid spacetimes 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 spacetime constitutes the freely specifiable initial data. Subject to Penrose’s Weyl Curvature Hypothesis, according to which the Weyl tensor was initially zero, it follows that the physical spacetime is Robertson-Walker. This may provide a basis for a new explanation for the large-scale isotropy of the universe.
Consideration is given to the Cauchy problem for perfect fluid spacetimes 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 spacetime constitutes the freely specifiable initial data. Subject to Penrose’s Weyl Curvature Hypothesis, according to which the Weyl tensor was initially zero, it follows that the physical spacetime is Robertson-Walker. This may provide a basis for a new explanation for the large-scale isotropy of the universe.
MSC:
| 53Z05 | Applications of differential geometry to physics |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
