Gravitational observables, intrinsic coordinates, and canonical maps

Abstract

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism transformations has remained obscure. In a symmetry-inspired approach we construct invariants out of canonically induced active gauge transformations. These invariants may be intepreted as the full set of dynamical variables evaluated in the intrinsic coordinate system. The functional invariants can explicitly be written as a Taylor expansion in the coordinates of any observer, and the coefficients have a physical and geometrical interpretation. Surprisingly, all invariants can be obtained as limits of a family of canonical transformations. This permits a short (again geometric) proof that all invariants, including the lapse and shift, satisfy Poisson brackets that are equal to the invariants of their corresponding Dirac brackets.

4 pages, to appear in Modern Physics Letters A

References in corpus (2)

• Large scale effective theory for cosmological bounces
• Revisiting observables in generally covariant theories in the light of gauge fixing methods

Cited by in corpus (8)

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• Synchronous coordinates and gauge-invariant observables in cosmological spacetimes
• Restoration of four-dimensional diffeomorphism covariance in canonical general relativity: An intrinsic Hamilton-Jacobi approach