MG11 
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York map, non-inertial frames and the physical interpretation of the gauge variables of the gravitational field

The explicit construction of the York map in ADM canonical gravity allows to make a clear separation of the tidal degrees of freedom of the gravitational field from its gauge variables. To get deterministic Hamilton equations for the tidal variables in globally hyperbolic spacetimes of the Christodoulou-Klainermann type, the gauge variables have to be fixed and this is equivalent to the determination of a global non-inertial frame. Since tha canonical Hamiltonian is the sum of the gauge-dependent weak ADM energy plus the constraints, all the gauge variables can be interpreted as relativistic inertial effects. The spacetime chronogeometrical structure is dynamically determined and there are indications that dark matter can be interpreted as a relativistic inertial effect when matter is present. This will require a background-independent weak field limit allowing to find a resummation of the PN 1/c expansions and the relativistic quadrupole emission formula.

Dynamical clock synchronization in Einstein's theory: implications for the ESA ACES mission

Given any solution of Einstein's equations in a coordinate system, the associated extrinsic curvature tensor in that coordinate system is uniquely determined. The 3+1 splitting of the spacetime, whose spacelike leaves have such an extrinsic curvature, can be determined with an inverse problem. The resulting leaves are both Cauchy surfaces for the given solution and simultaneity surfaces, namely a dynamical convention for the synchronization identifying a notion of instantaneous 3-space. The implications for the IAU conventions in the solar system and for the determination of the time delay of signals between an Earth station and the space station (to be measured in the ACES mission of ESA) are discussed

Dynamical clock synchronization in Einstein's theory: implications for the ESA ACES mission

Given any solution of Einstein's equations in a coordinate system, the associated extrinsic curvature tensor in that coordinate system is uniquely determined. The 3+1 splitting of the spacetime, whose spacelike leaves have such an extrinsic curvature, can be determined with an inverse problem. The resulting leaves are both Cauchy surfaces for the given solution and simultaneity surfaces, namely a dynamical convention for the synchronization identifying a notion of instantaneous 3-space. The implications for the IAU conventions in the solar system and for the determination of the time delay of signals between an Earth station and the space station (to be measured in the ACES mission of ESA) are discussed