The Rest-Frame Instant Form of Metric Gravity

TL;DR

This paper develops a rest-frame instant form of ADM canonical gravity for specific asymptotically flat spacetimes, clarifying the Hamiltonian structure and gauge transformations, and connecting to matter dynamics in Minkowski spacetime.

Contribution

It introduces a novel rest-frame instant form of metric gravity using Dirac's method, with added variables and constraints, for a class of spacetimes without supertranslations.

Findings

Defined the rest-frame instant form of ADM gravity.

Identified the Hamiltonian as the weak ADM energy.

Connected the framework to matter dynamics in Minkowski spacetime.

Abstract

In a special class of globally hyperbolic, topologically trivial, asymptotically flat at spatial infinity spacetimes selected by the requirement of absence of supertranslations (compatible with Christodoulou-Klainermann spacetimes) it is possible to define the {\it rest-frame instant form} of ADM canonical gravity by using Dirac's strategy of adding ten extra variables at spatial infinity and ten extra first class constraints implying the gauge nature of these variables. The final canonical Hamiltonian is the weak ADM energy and a discussion of the Hamiltonian gauge transformations generated by the eight first class ADM constraints is given. When there is matter and the Newton constant is switched off, one recovers the description of the matter on the Wigner hyperplanes of the rest-frame instant form of dynamics in Minkowski spacetime.