Gauge Theory of Gravity and Spacetime
arXiv:1204.3672
Abstract
The advent of general relativity settled it once and for all that a theory of spacetime is inextricably linked to the theory of gravity. From the point of view of the gauge principle of Weyl and Yang-Mills-Utiyama, it became manifest around the 1960s (Sciama--Kibble) that gravity is closely related to the Poincare group acting in Minkowski space. The gauging of this external group induces a Riemann-Cartan geometry on spacetime. If one generalizes the gauge group of gravity, one finds still more involved spacetime geometries. If one specializes it to the translation group, one finds a specific Riemann-Cartan geometry with teleparallelism (Weitzenbock geometry).
32 pages in latex, 2 figures; improved version in response to the referee reports, references updated and added
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Cited by in corpus (9)
- The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
- Gravitational Energy for GR and Poincare Gauge Theories: a Covariant Hamiltonian Approach
- The problem of space in the light of relativity: the views of H. Weyl and E. Cartan
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