Mathematics – Logic
Scientific paper
Dec 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phrvd..26.3359d&link_type=abstract
Physical Review D (Particles and Fields), Volume 26, Issue 12, 15 December 1982, pp.3359-3366
Mathematics
Logic
1
Scientific paper
A Hamiltonian formulation of anisotropic perfect-fluid-filled Kantowski-Sachs universes based on Demaret and Moncrief's unconstrained Arnowitt-Deser-Misner Hamiltonian is given; the canonical equations are derived and shown to be equivalent to the field equations, which proves the coherence of the reduction process. A canonical quantization method equivalent to the one previously used to quantize the perfect-fluid-filled diagonal Bianchi types I, V, and IX cosmological models is applied to the Kantowski-Sachs universes, leading to a Schrödinger equation for the wave function of these models and thus to a probability interpretation of the formalism. The density of probability of finding these universes in the classical singular state is shown to be zero for each barotropic equation of state of the type p=(γ-1)ρ (1<=γ<=2) apart from a set of measure zero of models corresponding to the stiff equation of state p=ρ.
Demaret Jacques
Hanquin Jean-Luc
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