Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-09-29
Class.Quant.Grav. 16 (1999) 3245-3262
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21 pages, no figures, LaTeX
Scientific paper
10.1088/0264-9381/16/10/315
Silent universes are studied using a ``3+1'' decomposition of the field equations in order to make progress in proving a recent conjecture that the only silent universes of Petrov type I are spatially homogeneous Bianchi I models. The infinite set of constraints are written in a geometrically clear form as an infinite set of Codacci tensors on the initial hypersurface. In particular, we show that the initial data set for silent universes is ``non-contorted'' and therefore (Beig and Szabados, 1997) isometrically embeddable in a conformally flat spacetime. We prove, by making use of algebraic computing programs, that the conjecture holds in the simpler case when the spacetime is vacuum. This result points to confirming the validity of the conjecture in the general case. Moreover, it provides an invariant characterization of the Kasner metric directly in terms of the Weyl tensor. A physical interpretation of this uniqueness result is briefly discussed.
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