Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-05-20
Class.Quant.Grav.25:235017,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Version Published in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/25/23/235017
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the relation between gravity and a general gauge theory. The dynamical variables are simply the frame field and the spin-connection pulled-back to the hypersurface, thereby eliminating the need for simplicity constraints on the momenta. A consequence of this is a degenerate (pre)symplectic form, which appears to be a necessary feature of the Einstein-Cartan formulation. A new feature unique to this approach arises when the constraint algebra is computed: the algebra is a deformation of the de Sitter, anti-de Sitter, or Poincar\'{e} algebra (depending on the value of the cosmological constant) with the deformation parameter being the conformal Weyl tensor.
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