Towards a general solution of the Hamiltonian constraints of General Relativity

Details Towards a general solution of the Hamiltonian constraints of General Relativity Towards a general solution of the Hamiltonian constraints of General Relativity

2005-10-17

arxiv.org/abs/gr-qc/0510080v2

Gen.Rel.Grav. 38 (2006) 1839-1859

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 Revtex pages, no figures. Modified version

Scientific paper

10.1007/s10714-006-0361-7

The present work has a double aim. On the one hand we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincar\'e Gauge Theory. On the other hand we study two kinds of solutions for the constraints of General Relativity, consisting of two mutually independent parts, namely a general three-metric-dependent contribution to the extrinsic curvature $K_{ab}$ in terms of the Cotton-York tensor, and besides it further metric independent contributions, which we analyze in particular in the presence of isotropic three-metrics.

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