Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity

TL;DR

This paper demonstrates how the Hamiltonian structure of General Relativity allows for a physical individuation of spacetime points and interprets the evolution of 3-spaces as a dynamic unfolding of simultaneity, offering a new conceptual perspective.

Contribution

It introduces a method to bypass the Hole Argument using Dirac observables and interprets the evolution of 3-spaces as a dynamical unfolding of simultaneity in GR.

Findings

The Hole Argument can be bypassed via physical individuation of spacetime points.

The chrono-geometric structure can be viewed as a global time unfolding of 3-spaces.

This approach offers a new conceptual framework distinct from standard SR views.

Abstract

The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold $M^4$ in terms of the "autonomous degrees of freedom" of the vacuum gravitational field ("Dirac observables"), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to "gauge" variables) of the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a "3-geometry" satisfying the relevant constraints on the Cauchy surface), can be interpreted as an "unfolding" in mathematical global time of a sequence of "achronal 3-spaces" characterized by "dynamically determined conventions" about distant simultaneity. This result stands out as an important "conceptual difference" with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an "endurantist" interpretations of ordinary "physical objects" in GR.