3+1 description of silent universes: a uniqueness result for the Petrov type I vacuum case

Silent universes are studied using a '3 + 1' decomposition of the held equa tions in order to make progress in proving a recent conjecture that the onl y silent universes of Petrov type I are spatially homogeneous Bianchi I mod els. The infinite set of constraints are written in a geometrically clear f orm as an infinite set of Codacci tensors on the initial hypersurface. In p articular, we show that the initial data set for silent universes is 'non-c ontorted' and therefore (Beig and Szabados 1997 Class. Quantum Grav. 14 309 1) isometrically embeddable in a conformally flat spacetime. We prove, by m aking use of algebraic computing programs, that the conjecture holds in the simpler case when the spacetime is vacuum. This result points to confirmin g the validity of the conjecture in the general case. Moreover, it provides an invariant characterization of the Kasner metric directly in terms of th e Weyl tensor. A physical interpretation of this uniqueness result is brief ly discussed.