Authors: E.P.J. de Haas
I start with a historical note on the galactic rotation curves issue. The problem with the virial theorem in observed galactic dynamics, lead to the Dark Matter hypothesis but also to Modified Newtonian Dynamics or MOND. Then I move (away) from MOND towards a relativistic, Lagrangian approach of orbital dynamics in a curved Schwarzschild metric. I propose a `constant Lagrangian' model for galactic scale geodetic dynamics. I will show with four rotation fitting curves to what extend my proposed model galaxies `constant Lagrangian' postulate works in these limited number of situations. The fitted galaxies are NGC 2403, NGC 3198, UGC 6614 and F571-8. In the paper I present a theoretical context in which the `constant Lagrangian' postulate might replace the classical virial theorem on a galactic scale. But the proposed postulate isn't a `general law of nature' because in the solar system and in the GNSS relativistic context, the classical virial theorem is proven accurate. Due to the limitations of the proposed postulate, a statement regarding Dark Matter can't be made. But the model might achieve within the GR-Schwarzschild paradigm what MOND achieves within the Newtonian paradigm, fitting the experimental galactic rotation curves.
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