  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
generalised 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 the
Riemann tensor. We comment briefly on implications for Mach principle.
