We complement the recent theory of Master Space-Teleparallel Supergravity (MS -TSG) 1, which reviews the acceleration and inertial effects, with two more consequences. We first address the “locality hypothesis” for extension of Lorentz invariance within Special Relativity to accelerated observers. This replaces the accelerated observer with a continuous infinity of hypothetical momentarily comoving inertial observers along its word line. This assumption is valid only if the curvature of the world line could be ignored. In the general case, this is actually untenable. In the framework of MS -TSG theory, the locality hypothesis introduces strict restrictions, replacing the curved MS with the flat MS . Our strategy, therefore, goes beyond the locality hypothesis to recover MS by invoking a general deformation MS , which, as a corollary, is solely responsible for acceleration and inertia effects. This significantly improves the standard metric and other relevant geometric structures referred to a noninertial frame in Minkowski space-time for relativistic velocities and arbitrary characteristic acceleration lengths. Second, we address the inertial effects in semi-Riemannian and more general post-Riemannian geometries. We derive the relativistic inertial force in semi-Riemannian space, and the inertial force acting on an extended rotating body moving in Riemann–Cartan space. The relativistic Weak Equivalence Principle is a consequence of the theory, at which inertial effects gradually decrease at large Lorentz factors and vanish in the photon limit.
G. Ter-Kazarian (Sun,) studied this question.