Post Newtonian limit of the Tensor-Vector-Scalar theory of gravity
General Relativity, Einstein’s celebrated theory of gravity, has so far passed all observational tests with flying colors; however, it is not the only conceivable theory of gravity, and quite a few alternatives have been proposed over the years, many merely as an intellectual exercise. In the weak field, slow motion limit, all theories of gravitation must coincide with Newton’s theory; it is in the post-Newtonian limit that they differ. This difference is quantified in the ten Parametrized Post-Newtonian parameters,
β, γ, ζ1, ζ2, ζ3, ζ4, ξ, α1, α2 and α3. Stringent experimental bounds exist for these parameters from solar system tests. General Relativity has β and γ unity, whereas all its other parameters are zero.
An alternative theory of gravity is TeVeS, designed by Bekenstein as a relativistic implementation of Milgrom’s Modified Newtonian Dynamics paradigm, which contrived to explain the flatness of galaxy rotation curves without assuming any Dark Matter. I will give an overview of TeVeS as a substitute for Dark Matter, and present my results on the Parametrized-Post-Newtonian parameters for TeVeS, which show that for certain values of the coupling constants of the theory, TeVeS is indiscernible from General Relativity in the solar system, and is thus a viable theory of gravity.