General Covariance and its Implications for Einstein's Space-Times
Abstract
Description
This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and tetrad gravity are analyzed in a class of space-times suitable to incorporate particle physics by using Dirac theory of constraints, which allows to arrive at a separation of the genuine degrees of freedom of the gravitational field, the Dirac observables describing generalized tidal effects, from its gauge variables, describing generalized inertial effects. A background-independent formulation (the rest-frame instant form of tetrad gravity) emerges, since the chosen boundary conditions at spatial infinity imply the existence of an asymptotic flat metric. By switching off the Newton constant in presence of matter this description deparametrizes to the rest-frame instant form for such matter in the framework of parametrized Minkowski theories. The problem of the objectivity of the space-time point-events, implied by Einstein's Hole Argument, is analyzed.
Talk at the Meeting {\it La Relativita' dal 1905 al 2005: passato, presente e futuro} organized by SIGRAV and SISM, Department of Mathematics of the Torino University, June 1, 2005; at ERE2005 {\it A century of relativity physics}, XXVIII Spanish Relativity Meeting, Oviedo, September 6-10, 2005; at QG05 {\it Constrained dynamics and quantum gravity 05}, Cala Gonone (Sardinia, Italy), September 12-16, 2005 Some typo errors and some references are corrected
Talk at the Meeting {\it La Relativita' dal 1905 al 2005: passato, presente e futuro} organized by SIGRAV and SISM, Department of Mathematics of the Torino University, June 1, 2005; at ERE2005 {\it A century of relativity physics}, XXVIII Spanish Relativity Meeting, Oviedo, September 6-10, 2005; at QG05 {\it Constrained dynamics and quantum gravity 05}, Cala Gonone (Sardinia, Italy), September 12-16, 2005 Some typo errors and some references are corrected