Relativistic fermions in designer curved space
However, already in the Solar System, the instantaneous 3‐spaces are not Euclidean in the selected solutions, but the existing technology is not yet able to show it, being a property of order O ( 1 / c 2 ) 3
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These frames are compatible with the usual interpretation as quasi‐inertial framesin Minkowski space‐time and are metrology choices like the choice of a certain atomic clock as standard of time. for a review of the existing conventions in the Solar System.Īccording with the International Astronomic Union IAU inside the Solar System, the choice of the 4‐coordinates is solved at the experimental level by the choice of a convention for the description of matterbased on special post‐Newtonian (PN) solutions of linearized Einstein equations in a fixed given harmonic gauge : (a) for satellites near the Earth (like the GPS ones) one uses NASA 4‐coordinates compatible with the reference frames of the International Terrestrial Reference System ITRS2003 2 and of the Geocentric Celestial Reference System GCRS IAU2000 (b) for planets in the Solar System one uses the frame of the Barycentric Celestial Reference System BCRS‐IAU2000.
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An extremely important, till now not explicitly clarified, point in Einstein general relativity (GR) (and in every generally covariant theory of gravity), whose gauge group is the group of diffeomorphisms of the Lorentzian 4‐dimensional space‐time, 1 is that the fixation of the gauge freedom is nothing else than the establishment of conventions for relativistic metrology, an operation performed from atomic physicists, NASA engineers and astronomers with the introduction of a notion of clock synchronization and with a definition of the axes for the 4‐coordinates in each point, that is, with the identification of a non‐inertial frame of the space‐time (global inertial frames are forbidden by the equivalence principle).