Relativistic dynamics in regions of extremely small accelerations

Abstract

We reexamine the lack of conserved quantities in the original formulation of Modified Newtonian Dynamics (MoND) from the viewpoint of the special theory of relativity. Lorentz invariant expressions for momentum and energy consistent with the Tully-Fisher Law are employed to address the dynamics of a particle entering a region of extremely small accelerations but with possibly relativistic speed. The results of the Alternative MoND proposed recently by Romero and Zamora are shown to follow from these in the non-relativistic limit.