Gravitational coupling of Klein-Gordon and Dirac particles to matter vorticity and spacetime torsion

Abstract

The authors examine the gravitational coupling of Klein-Gordon and Dirac fields to matter vorticity and spacetime torsion, in the context of Einstein-Cartan theory. The background spacetime is endowed with a Godel-type metric, characterized by two real parameters ( Omega , l2); the source of spacetime curvature is a Weyssenhoff-Raabe fluid with spin vector parallel to the vorticity field. They show that torsion and matter vorticity have identical effects on the physics of particle fields. Complete sets of solutions are obtained, satisfying boundary conditions connected to the test-field character of the solutions. The energy spectrum obtained is discrete in general, except for the case of hyperbolic Godel-type geometries (l2>0) where a continuum region in the energy spectrum may appear: if 0< Omega 2<l2 a continuum region is present in the upper part of the spectrum; if Omega 2>or=l2, Dirac solutions may present, under certain conditions, a continuum region in the lower part of the spectrum. The correspondence between classical geodesic motion and Klein-Gordon solutions is established, and used as a guide to select the correct boundary conditions for the test fields. Matter vorticity and/or spacetime torsion split the energy spectrum of Dirac particles. These effects are additive and result from the existence of the same constant of motion for both cases. This constant of motion generates a trivial symmetry of the system in Minkowski spacetime, the associated degeneracy of which is raised by matter vorticity and/or torsion fields, producing the above-mentioned split.