Gravitational Constraint Combinations Generate a Lie Algebra

Details Gravitational Constraint Combinations Generate a Lie Algebra Gravitational Constraint Combinations Generate a Lie Algebra

1996-01-23

arxiv.org/abs/gr-qc/9601038v2

Class.Quant.Grav. 13 (1996) 2577

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, latex, submitted to Classical and Quantum Gravity. Section 3 is expanded and an additional solution provided, minor

Scientific paper

10.1088/0264-9381/13/9/021

We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of finding alternative constraints for canonical gravity. The new scalars may be used in place of the hamiltonian constraint of general relativity and, together with the usual momentum constraints, replace the Dirac algebra for pure gravity with a true Lie algebra: the semidirect product of the Abelian algebra of the new constraint combinations with the algebra of spatial diffeomorphisms.

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