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General Covariance and the Objectivity of Space-Time Point-Events: The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity | | Luca Lusanna
; Massimo Pauri
; | | Date: |
10 Dec 2002 | | Subject: | gr-qc astro-ph hep-th | | Affiliation: | INFN, Firenze) and Massimo Pauri (Univ. Parma | | Abstract: | (Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the {it weak} ADM energy. The main results of the investigation are the following: 1) A re-interpretation of {it active} diffeomorphisms as {it passive and metric-dependent} dynamical symmetries of Einstein’s equations, a re-interpretation that discloses their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the {it Hole Argument}. 2) The utilization of Bergmann-Komar {it intrinsic coordinates} for a peculiar gauge-fixing to the superhamiltonian and supermomentum constraints which embodies on shell a {it physical individuation} of the mathematical points of $M^4$ as point-events in terms of the non-local intrinsic degrees of freedom of the gravitational field (Dirac observables). 3) A clarification of the notion of {it Bergmann observable} that leads to a main conjecture asserting the existence of i) special Dirac observables which are also Bergmann observables; ii) tensorial (scalar) gauge variables. | | Source: | arXiv, gr-qc/0301040 | | Services: | Forum | Review | PDF | Favorites | |
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