General Relativity as a Theory of Two Connections

Details General Relativity as a Theory of Two Connections General Relativity as a Theory of Two Connections

1993-10-04

arxiv.org/abs/gr-qc/9310009v1

Int.J.Mod.Phys.D3:379-392,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, LATEX, Preprint CGPG-93/09-5

Scientific paper

10.1142/S0218271894000587

We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two $SO(3)$ connections. We analyze first the Husain-Kucha\v{r} model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the Ashtekar one, from which it is derived, but has some interesting features of its own. Among them a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of General Relativity.

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