  A tensor description of perturbative Einsteinian gravity about an arbitrary
background spacetime is developed. By analogy with the covariant laws of
electromagnetism in spacetime, gravito-electromagnetic potentials and fields
are defined to emulate electromagnetic gauge transformations under
substitutions belonging to the gauge symmetry group of perturbative
gravitation. These definitions have the advantage that on a flat background,
with the aid of a covariantly constant timelike vector field, a subset of the
linearised gravitational field equations can be written in a form that is fully
analogous to Maxwell's equations (without awkward factors of 4 and extraneous
tensor fields). It is shown how the remaining equations in the perturbed
gravitational system restrict the time dependence of solutions to these
equations and thereby prohibit the existence of propagating vector fields. The
induced gravito-electromagnetic Lorentz force on a test particle is evaluated
in terms of these fields together with the torque on a small gyroscope. It is
concluded that the analogy of perturbative gravity to Maxwell's description of
electromagnetism can be valuable for (quasi-)stationary gravitational phenomena
but that the analogy has its limitations.
