Topological invariants and the dynamics of an axial vector torsion field

Details Topological invariants and the dynamics of an axial vector torsion field Topological invariants and the dynamics of an axial vector torsion field

Aug 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983gregr..15..703d&link_type=abstract

General Relativity and Gravitation, Volume 15, Issue 8, pp.703-723

Physics

9

Scientific paper

A generalized theory of gravitation is discussed which is based on a Riemann-Cartan space-time,U 4, with an axial vector torsion field. Besides Einstein's equations determining the metric of theU 4, a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for theU 4 space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic.

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