Metric-connection theories of gravity
In this thesis I study the metric-connection theories of gravity. I am mostly concerned with theories whose connection cannot be completely specified in terms of the metric. Although I sometimes consider completely general connections, I often restrict my attention to Cartan connections (metric-compatible but nontorsion-free). In the context of metric-Cartan connection theories, I try to answer the question, is the torsion observable. Using a method similar to that used by Papapetrou and Dixon in the context of metric theories, I derive propagation equations for a body's momentum and angular momentum. These show that elementary particle spins feel the torsion but orbital angular momentum does not. However, the measurement of the effect of torsion on spin is beyond present technology. As a corollary, I prove that in a metric theory, spin and orbital angular momentum propagate in the same way. I develop a two tangent space formalism which gives geometrical insight into the presence of two connections. As an example of a computation using the two tangent space formalism, I rederive the conservation laws of energy-momentum and angular momentum by applying Noether's theorem to coordinate an 0(3,1,R)-frame invariance. Considering GL-(4,R)-frame invariance, I also obtain conservation laws for hypermomentum and dilation current. To understand the dynamics of gravitational fields, one must choose gravitational field equations. I restrict my attention to field equations which involve no higher than second derivatives of the orthonormal frame and a Cartan connection. I show that there is a twelve parameter family of such theories whose Lagrangians are quadratic polynomials in the Cartan curvature and torsion.
- Research Organization:
- Maryland Univ., College Park (USA)
- OSTI ID:
- 5435195
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
Lagrange multipliers in theories of gravitation
Geometrical theory of spin motion