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  • Print publication year: 2019
  • Online publication date: June 2019

6 - ADM Tetrad Gravity and Its Constraints

from Part II - General Relativity: Globally Hyperbolic Einstein Space-Times

Summary

In the chosen family of Einstein space-times one can give an ADM formulation of tetrad gravity and of its first-class constraints, so that fermions can be described in this framework. There are 16 configuration variables, 16 momenta, and 14 first-class constraints. Then one can define a new canonical basis adapted to 10 of the 14 constraints (not to the super-Hamiltonian and super-momentum ones) with a Shanmugadhasan canonical transformation. This allows identifying two pairs of canonical variables describing the tidal effects (the gravitational waves after linearization). However, they are not Dirac observables.