Constraints on ADM tetrad gravity parameter space from S2 star in the center of the Galaxy and from the Solar System

ADM tetrad gravity is an Hamiltonian reformulation of General Relativity which gives new insight to the Dark Matter Problem. We impose constraints on the parameter space of ADM tetrad gravity with a Yukawa-like ansatz for the trace of the extrinsic curvature of the 3D hypersurfaces by fitting the orbit of the S2 star around the Black Hole in the Galactic center and using the perihelia of some of the planets of the Solar System. We find very thight constraints on the \emph{strength} of the coupling, $4.2 \,\times \, 10^{-4} \, \text{AU}\,\lesssim \, δ\, \lesssim \, 4.6 \, \times \, 10^{-4} \, \text{AU}$, and an upper limit for the (inverse) scale length, $μ\, \lesssim \, 3.5 \, \times \, 10^{-6} \, \text{AU}^{-1}$.

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