The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation

Details The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation

1993-07-08

arxiv.org/abs/gr-qc/9307006v1

Nucl.Phys.B415:515-532,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, preprint# SU-GP-93/64

Scientific paper

10.1016/0550-3213(94)90121-X

The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the 2-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions to the field equations. In the process we find two new systems of first class constraints which describe part of the degenerate sectors of the Ashtekar formulation. One of them also generalizes the Witten constraints. Finally we argue that the Ashtekar formulation has an arbitrarily large number of degrees of freedom in contrast to the usual descriptions. TO GET THE FIGURES CONTACT Barbero@suhep.phy.syr.edu or Madhavan@suhep.phy.syr.edu

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