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

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Relativity and the Dimensionality of the World

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 153))

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 4in 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).

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  1. INFN Firenze, Italy

    Luca Lusanna

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  1. Luca Lusanna
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  1. Concordia University, Montreal, QC, Canada

    Vesselin Petkov

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Lusanna, L., Pauri, M. (2007). Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity. In: Petkov, V. (eds) Relativity and the Dimensionality of the World. Fundamental Theories of Physics, vol 153. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6318-3_13

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