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In canonical tetrad gravity, it is possible to identify the gauge variables, describing relativistic inertial effects, in Einstein general relativity. One of these is the York time, the trace of the extrinsic curvature of the instantaneous non-Euclidean 3-spaces (global Euclidean 3spaces are forbidden by the equivalence principle). The extrinsic curvature depends both on gauge variables and on dynamical ones like the gravitational waves after linearization. The fixation of these gauge variables is done by relativistic metrology with its identification of time and space. Till now, the International Celestial Reference Frame ICRF uses Euclidean 3-spaces outside the Solar System. It is shown that York time and non-Euclidean 3-spaces may explain the main signatures of dark matter in ordinary space-time before using cosmology. Also dark energy may be connected to these inertial gauge effects, because both red-shift and luminosity distance depend on them.

Relativistic Celestial Metrology: Dark Matter as an Inertial Gauge Effect