E. Cartan moment of rotation in Ashtekar's self-dual representation of gravitation
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205 (United States)
- T-6 Group, Theoretical Division, MS B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
The geometric construction of the E. Cartan moment of rotation associated to the spacetime curvature provides a geometric interpretation of the gravitational field sources and describes geometrically how the sources are wired'' to the field in standard geometrodynamics. The E. Cartan moment of rotation yields an alternate way (as opposed to using variational principles) to obtain Einstein equations. The E. Cartan construction uses, in an essential way, the soldering structure of the frame bundle underlying the geometry of the gravitational field of general relativity. The geometry of Ashtekar's connection formulation of gravitation is based on a complex-valued self-dual connection that is not defined on the frame bundle of spacetime. It is shown how to transfer the construction of the E. Cartan moment of rotation of Ashtekar's formulation of the theory of gravity and demonstrate that no spurious equations are produced via this procedure.
- OSTI ID:
- 6991674
- Journal Information:
- Journal of Mathematical Physics (New York); (United States), Vol. 33:6; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Cartan gravity, matter fields, and the gauge principle
Austerity and geometric structure of field theories
Related Subjects
GENERAL PHYSICS
GRAVITATIONAL FIELDS
DIFFERENTIAL GEOMETRY
EINSTEIN FIELD EQUATIONS
GENERAL RELATIVITY THEORY
QUANTUM GRAVITY
RIEMANN SPACE
SPACE-TIME
SPINORS
VARIATIONAL METHODS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GEOMETRY
MATHEMATICAL SPACE
MATHEMATICS
QUANTUM FIELD THEORY
SPACE
661310* - Relativity & Gravitation- (1992-)