Novel Ansatzes and Scalar Quantities in Gravito-Electromagnetism
  In this work, we focus on the theory of Gravito-Electromagnetism (GEM) -- the
theory that describes the dynamics of the gravitational field in terms of
quantities met in Electromagnetism -- and we propose two novel forms of metric
perturbations. The first one is a generalisation of the traditional GEM ansatz,
and succeeds in reproducing the whole set of Maxwell's equations even for a
dynamical vector potential A. The second form, the so-called alternative
ansatz, goes beyond that leading to an expression for the Lorentz force that
matches the one of Electromagnetism and is free of additional terms even for a
dynamical scalar potential \Phi. In the context of the linearised theory, we
then search for scalar invariant quantities in analogy to Electromagnetism. We
define three novel, 3rd-rank gravitational tensors, and demonstrate that the
last two can be employed to construct scalar quantities that succeed in giving
results very similar to those found in Electromagnetism. Finally, the gauge
invariance of the linearised gravitational theory is studied, and shown to lead
to the gauge invariance of the GEM fields E and B for a general configuration
of the arbitrary vector involved in the coordinate transformations.
