Noninertial frames that can mimic gravitational fields

One version of the principle of equivalence, as originally formulated by Einstein, states that ``gravity'' can be mimicked locally by going to an ``accelerated frame of reference.'' As highlighted by Synge, the physical content of this principle remains obscure in so far as it does not refer to the Riemann tensor ${R}_{abcd}$, which encodes the true effects of gravity. We here give the acceleration profile of a Born rigid, Rindler esque, frame that can mimic a gravitational field corresponding to a given ${R}_{abcd}$. The generalized deviation equation that yields this result also has centrifugal and Coriolis terms appearing in a purely relational context, yielding a similar connection between angular velocity of rotating, rigid inertial frames and Riemann. We comment briefly on implications for the Mach principle.