Gravitational Constraint Combinations Generate a Lie Algebra

Abstract

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 Kuchař 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.

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

References in corpus (3)

• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Action functionals for relativistic perfect fluids
• Gravitational Constraints which Generate a Lie Algebra

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• Null dust in canonical gravity
• Constraints Algebra and Equations of Motion in Bohmian Interpretation of Quantum Gravity
• Time evolution in deparametrized models of loop quantum gravity
• Dirac and Lagrangian reductions in the canonical approach to the first order form of the Einstein-Hilbert action
• The Tetrad Frame Constraint Algebra
• Geometrodynamics in a spherically symmetric, static crossflow of null dust