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(abridged)The achievements of the present work include: a) A clarification ofthe multiple definition given by Bergmann of the concept of {\it (Bergmann)observable. This clarification leads to the proposal of a {\it main conjecture}asserting the existence of i) special Dirac's observables which are alsoBergmann's observables, ii) gauge variables that are coordinate independent(namely they behave like the tetradic scalar fields of the Newman-Penroseformalism). b) The analysis of the so-called {\it Hole} phenomenology in strictconnection with the Hamiltonian treatment of the initial value problem inmetric gravity for the class of Christoudoulou -Klainermann space-times, inwhich the temporal evolution is ruled by the {\it weak} ADM energy. It iscrucial the re-interpretation of {\it active} diffeomorphisms as {\it passiveand metric-dependent} dynamical symmetries of Einstein's equations, are-interpretation which enables to disclose their (nearly unknown) connectionto gauge transformations on-shell; this is expounded in the first paper(gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsicpseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinatesystems for the 4-dimensional {\it mathematical} manifold, in terms of thehighly non-local degrees of freedom of the gravitational field (its fourindependent {\it Dirac observables}), and to realize the {\it physicalindividuation} of the points of space-time as {\it point-events} as agauge-fixing problem, also associating a non-commutative structure to each4-coordinate system.Comment: 41 pages, Revtex

general relativity and gravitation

The physical role of gravitational and gauge degrees of freedom in general relativity – II: Dirac versus Bergmann observables and the objectivity of space-time