The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects

Abstract

This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results concerning specific issues, and for new insights about \emph{old} foundational problems of the theory. The first paper includes: 1) a critical analysis of the various concepts of symmetry related to the Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian viewpoint, on the other. This analysis leads, in particular, to a re-interpretation of {\it active} diffeomorphisms as {\it passive and metric-dependent} dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose the (nearly unknown) connection of a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a re-visitation of the canonical reduction of the ADM formulation of general relativity, with particular emphasis on the geometro-dynamical effects of the gauge-fixing procedure, which amounts to the definition of a \emph{global (non-inertial) space-time laboratory}. This analysis discloses the peculiar \emph{dynamical nature} that the traditional definition of distant simultaneity and clock-synchronization assume in general relativity, as well as the {\it gauge relatedness} of the "conventions" which generalize the classical Einstein's convention.

45 pages, Revtex4, some refinements added

References in corpus (5)

• The Many Faces of Gravitoelectromagnetism
• The Rest-Frame Instant Form of Metric Gravity
• A New Parametrization for Tetrad Gravity
• Hamiltonian linearization of the rest-frame instant form of tetrad gravity in a completely fixed 3-orthogonal gauge: a radiation gauge for background-independent gravitational waves in a post-Minkowskian Einstein spacetime
• Constructing Solutions of the Einstein Constraint Equations

Cited by in corpus (7)

• Revisiting observables in generally covariant theories in the light of gauge fixing methods
• Generalized Radar 4-Coordinates and Equal-Time Cauchy Surfaces for Arbitrary Accelerated Observers
• Gauge invariant method for maximum simplification of the field strength in non-Abelian Yang-Mills theories
• On the Meaning of the Principle of General Covariance
• Dark Matter as a Relativistic Inertial Effect in Einstein Canonical Gravity?
• On the nature of the new group LB1
• Relativistic Entanglement from Relativistic Quantum Mechanics in the Rest-Frame Instant Form of Dynamics