York Map, Non-Inertial Frames and the Physical Interpretation of the Gauge Variables of the Gravitational Field

Details York Map, Non-Inertial Frames and the Physical Interpretation of the Gauge Variables of the Gravitational Field York Map, Non-Inertial Frames and the Physical Interpretation of the Gauge Variables of the Gravitational Field

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008mgm..conf.2481l&link_type=abstract

"THE ELEVENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation an

Physics

Scientific paper

While in Newtonian physics space and time are absolute notions, in special relativity (SR) only space-time (with its conformal structure identified by incoming and outgoing rays of light) is absolute. Any notion of instantaneous 3-space and of spatial distance is observer- and frame-dependent, since it is determined by the arbitrary choice of a convention for the synchronization of distant clocks done by a time-like observer. Given the observer and the convention, a Møller-admissible 3+1 splitting of Minkowski space-time (and therefore a (in general) non-inertial frame centered on the observer) is obtained.1 It is convenient to use radar 4-coordinates (τ, σr) adapted to the 3+1 splitting: τ is observer proper time and σr are curvilinear 3-coordinates on each equal-time 3-surface Στ with origin on observer's world-line. In the framework of parametrized Minkowski theories,2 the dynamics of every isolated system admitting a Lagrangian formulation is formulated in such a way that the change of the clock synchronization convention is a gauge transformation. The rest-frame instant form of dynamics is associated with the inertial 3+1 splitting whose instantaneous 3-spaces are orthogonal to the conserved 4-momentum of the isolated system...

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