The York Map and the Role of Non-Inertial Frames in the Geometrical View of the Gravitational Field

TL;DR

This paper clarifies the role of non-inertial frames in general relativity using Dirac's constraints, identifying gauge variables as inertial effects and Dirac observables as tidal effects, with York time controlling clock synchronization.

Contribution

It introduces a York canonical basis that interprets gauge variables as inertial effects and identifies Dirac observables as tidal effects in the gravitational field.

Findings

York time controls clock synchronization.

Instantaneous 3-spaces are dynamically determined.

Gauge variables represent generalized inertial effects.

Abstract

The role of non-inertial frames in a class of models of general relativity is clarified by means of Dirac's theory of constraints. The identification of a York canonical basis allows to give the interpretation of the gauge variables as generalized inertial effects and to identify the Dirac observables of the gravitational field with generalized tidal effects. York time is the gauge variable controlling the clock synchronization convention. Differently from special relativity, the instantaneous 3-spaces are dynamically determined.