Spatially homogeneous neutrino cosmologies

Journal Article · Tue Jul 01 04:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524613· OSTI ID:5332909

Michalik, T R; Melvin, M A

Gravitational effects of a c number neutrino field in spatially homogeneous geometries are analyzed. At the basis of the description of the geometries is an arbitrary timelike congruence with aligned tetrad reference frames, i.e., one basis vector of the tetrad frame at each point of space--time is aligned along the congruence. The remaining three basis vectors of the tetrad lie in orthogonal spacelike hypersurfaces, and for these there are three alternative choices: (1) invariant reference triads, i.e., which conform to the isometry group of the space with structure constants G/sup c//sub g/h; (2) orthonormal reference triads simulating a Euclidean structure at each point; (3) holonomic coordinate triads in terms of which metrics are usually given. The relations between (1), (2), and (3) for all nine Bianchi--Behr types are reviewed. The relatively compact vector--dyadic formalism used by Estabrook, Wahlquist, and Behr is introduced; it has the advantage that it gives directly the Bianchi--Behr classification of cosmologic solutions, and represents these solutions in terms of the orthonormal frame components of interesting physical quantities such as shear rates, volume expansion rates, and rotation with respect to inertially stabilized directions. The coupled Einstein--Dirac equations for the gravitational neutrino field and the neutrino stress-energy tensor are derived, and the coupling equations are replaced by a set in which the neutrino amplitude is eliminated, and instead there appear the neutrino current (J, J/sub 0/=vertical-barJvertical-bar) (vector bilinear covariant) and the ''eikonal momentum'' P=del f, the gradient of the phase function f(x) which appears in the neutrino spinor amplitude psi=chi(t)e/sup i/f(x). Solutions for all nine Bianchi types are classified.

• Research Organization: Randolph--Macon Woman's College, Lynchburg, Virginia 24504
• OSTI ID: 5332909
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMOLOGICAL MODELS
COUPLING
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EINSTEIN FIELD EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
LEPTONS
MASSLESS PARTICLES
MATHEMATICAL MODELS
NEUTRINOS
QUANTUM FIELD THEORY
SPACE-TIME
SPINORS
WAVE EQUATIONS
WAVE FUNCTIONS