Current searches for signals of departures from the fundamental symmetries of
General Relativity using gravitational waves are largely dominated by
propagation effects like dispersion and birefringence from highly dynamic
sources such as coalescing binary-black holes and neutron stars. In this paper
we take steps towards probing the nature of spacetime symmetries in the
generation stage of gravitational waves; by using a generic effective-field
theory, we solve the modified Einstein equations order-by-order for a generic
source, and we write down the the first Post-Newtonian corrections, which
includes contributions from the spacetime-symmetry breaking terms. Choosing as
the source a system of point particles allows us to write down a simple toy
solution explicitly, and we see that in contrast to General Relativity, the
monopolar and dipolar contributions are non-vanishing. We comment on the
detectability of such signals by the Laser Interferometer Space Antenna (LISA)
space mission, which has high signal-to-noise galactic binaries (which can be
modelled as point particles) well inside its predicted sensitivity band,
sources which are inaccessible for current ground-based detectors, and we also
discuss the possibility of going beyond the quadrupole formula and the first
Post-Newtonian order, which would reveal effects which could be probed by
ground-based detectors observing coalescence events.Comment: 14 pages, 3 figure