The Initial Value Problem in Light of Ashtekar's Variables

Details The Initial Value Problem in Light of Ashtekar's Variables The Initial Value Problem in Light of Ashtekar's Variables

1993-02-18

arxiv.org/abs/gr-qc/9302020v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, UMDGR93-140, NSF-ITP-93-20

Scientific paper

The form of the initial value constraints in Ashtekar's hamiltonian formulation of general relativity is recalled, and the problem of solving them is compared with that in the traditional metric variables. It is shown how the general solution of the four diffeomorphism constraints can be obtained algebraically provided the curvature is non-degenerate, and the form of the remaining (Gauss law) constraints is discussed. The method is extended to cover the case when matter is included, using an approach due to Thiemann. The application of the method to vacuum Bianchi models is given. The paper concludes with a brief discussion of alternative approaches to the initial value problem in the Ashtekar formulation.

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