Relativistic Generalized Inertia: From Post-Newtonian Dynamicsto Galactic Rotation Curves

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Abstract
In General Relativity (GR), both branches of the conservation law ∇μTμν = 0 involve the samecombination, the inertial mass density (IMD) I = ρ+p. In cosmology, it can be probed only through the energy-conservation branch, where its parametrization underlies dynamical dark-energy models, whereas in the momentum-conservation branch it is the quantity multiplying the acceleration. Motivated by this consideration, we develop a relativistic generalized-inertia (RGI) framework to the first post-Newtonian (PN) order, in which the inertial response of matter is generalized but the gravitational dynamics of GR remain unchanged. The contributions of pressure and gravitational self-energy to the PN inertial mass density are weighted by two phenomenological parameters, α and β. It is shown that this generalization results in a difference between the inertial, passive, and activegravitational masses and gives rise to a kinematic Nordtvedt effect and momentum non-conservation. We place limits on these parameters by means of Lunar Laser Ranging and by using observations of binary and triple millisecond pulsars, along with constraints derived from linear-momentum conservation. We then investigate the implications of the framework for galactic dynamics.

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