General Covariance and its Implications for Einstein's Space-Times

TL;DR

This paper reviews the structure of spacetime in relativity, focusing on non-inertial frames, clock synchronization, and the canonical formulation of gravity, highlighting the separation of physical degrees of freedom from gauge variables.

Contribution

It introduces a background-independent formulation of tetrad gravity with boundary conditions at infinity, clarifying the physical degrees of freedom and inertial effects in spacetime.

Findings

Separation of gravitational degrees of freedom from gauge variables.

Emergence of a background-independent, rest-frame formulation of gravity.

Analysis of the objectivity of space-time point-events in relativity.

Abstract

This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and tetrad gravity are analyzed in a class of space-times suitable to incorporate particle physics by using Dirac theory of constraints, which allows to arrive at a separation of the genuine degrees of freedom of the gravitational field, the Dirac observables describing generalized tidal effects, from its gauge variables, describing generalized inertial effects. A background-independent formulation (the rest-frame instant form of tetrad gravity) emerges, since the chosen boundary conditions at spatial infinity imply the existence of an asymptotic flat metric. By switching off the Newton constant in presence of matter this description deparametrizes to the rest-frame instant form for such matter in the framework of parametrized Minkowski theories. The problem of the objectivity of the space-time point-events, implied by Einstein's Hole Argument, is analyzed.