Torsion waves in metric-affine field theory

Details Torsion waves in metric-affine field theory Torsion waves in metric-affine field theory

2000-12-13

arxiv.org/abs/gr-qc/0012046v1

Class.Quant.Grav. 18 (2001) 2317-2330

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX2e

Scientific paper

10.1088/0264-9381/18/12/307

The approach of metric-affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the unknowns of the theory. We write the Yang-Mills action for the affine connection and vary it both with respect to the metric and the connection. We find a family of spacetimes which are stationary points. These spacetimes are waves of torsion in Minkowski space. We then find a special subfamily of spacetimes with zero Ricci curvature; the latter condition is the Einstein equation describing the absence of sources of gravitation. A detailed examination of this special subfamily suggests the possibility of using it to model the neutrino. Our model naturally contains only two distinct types of particles which may be identified with left-handed neutrinos and right-handed antineutrinos.

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