Canonical Reduction of Gravity: from General Covariance to Dirac Observables and post-Minkowskian Background-Independent Gravitational Waves

TL;DR

This paper reviews the canonical reduction of metric and tetrad gravity in asymptotically Minkowskian space-times, deriving background-independent gravitational waves as solutions of linearized Hamilton equations without background assumptions.

Contribution

It introduces a Hamiltonian linearization in a fixed gauge for asymptotically flat space-times, leading to a background-independent formulation of gravitational waves.

Findings

Background-independent gravitational waves derived as solutions of linearized Hamilton equations.

Canonical reduction achieved without introducing a background metric.

Framework applicable to Christodoulou-Klainermann type space-times.

Abstract

The status of canonical reduction for metric and tetrad gravity in space-times of the Christodoulou-Klainermann type, where the ADM energy rules the time evolution, is reviewed. Since in these space-times there is an asymptotic Minkowski metric at spatial infinity, it is possible to define a Hamiltonian linearization in a completely fixed (non harmonic) 3-orthogonal gauge without introducing a background metric. Post-Minkowskian background-independent gravitational waves are obtained as solutions of the linearized Hamilton equations.