  We discuss an approach to gravitational waves based on Geometric Algebra and
Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we
consider Gauge Theory Gravity, which uses symmetries expressed within the GA of
flat spacetime to derive gravitational forces as the gauge forces corresponding
to making these symmetries local. We then consider solutions for black holes
and plane gravitational waves in this approach, noting the simplicity that GA
affords in both writing the solutions, and checking some of their properties.
We then go on to show that a preferred gauge emerges for gravitational plane
waves, in which a `memory effect' corresponding to non-zero velocities left
after the passage of the waves becomes clear, and the physical nature of this
effect is demonstrated. In a final section we present the mathematical details
of the gravitational wave treatment in GA, and link it with other approaches to
exact waves in the literature. Even for those not reaching it via Geometric
Algebra, we recommend that the general relativity metric-based version of the
preferred gauge, the Brinkmann metric, be considered for use more widely by
astrophysicists and others for the study of gravitational plane waves. These
advantages are shown to extend to a treatment of joint gravitational and
electromagnetic plane waves, and in a final subsection, we use the exact
solutions found for particle motion in exact impulsive gravitational waves to
discuss whether backward in time motion can be induced by strongly non-linear
waves.
