  Mishra has recently established, using a generic static metric, the relative
local proper-time 3-acceleration of a test-particle in one-dimensional free
fall relative to a static reference frame in any static spacetime. In this
paper, on the grounds of gravitoelectromagnetism we establish, in a covariant
spacetime form, the relative 4-acceleration for the general free fall,
indicating its canonical representation with its 3-space cinematical content.
Then we obtain the relation between this representation and the very known
expression for the relative free fall acceleration in Fermi coordinates. Taking
this into account, it is shown that an experiment with relativistic beams in a
circular accelerator, modelled by Fermi coordinates, recently proposed by
Moliner et al, can test the here established covariant result and, therefore,
can also verify Mishra's formula. This possibility of experimental
verification, besides its intrinsic importance, can answer a recent inquire by
Vigier, related to his recent proposal of derivation of inertial forces.
