The symplectic 2-form for gravity in terms of free null initial data

Abstract

A hypersurface formed of two null sheets, or "light fronts", swept out by the future null normal geodesics emerging from a common spacelike 2-disk can serve as a Cauchy surface for a region of spacetime. Already in the 1960s free (unconstrained) initial data for general relativity were found for such hypersurfaces. Here an expression is obtained for the symplectic 2-form of vacuum general relativity in terms of such free data. This can be done, even though variations of the geometry do not in general preserve the nullness of the initial hypersurface, because of the diffeomorphism gauge invariance of general relativity. The present expression for the symplectic 2-form has been used previously to calculate the Poisson brackets of the free data.

44 pages, 2 figures

References in corpus (4)

• The Dynamics of General Relativity
• The Poisson bracket on free null initial data for gravity
• Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors
• The symplectic 2-form and Poisson bracket of null canonical gravity

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• Gravity Degrees of Freedom on a Null Surface
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• First order gravity on the light front
• Quantum Null Geometry and Gravity
• Sachs' free data in real connection variables
• The Poisson brackets of free null initial data for vacuum general relativity
• Integrable structures and the quantization of free null initial data for gravity
• Gravitational Constraints on a Lightlike boundary
• Evidence for Planck Luminosity Bound in Quantum Gravity
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Scale Invariance in Gravity On The Light-Front