Gravitational Wave Polarization and Test Particles
This Demonstration shows how test particles move when a gravitational wave passes them. The wave is perpendicular to the plane of the particles. The two polarizations are "plus" polarization and "cross" polarization, 45° apart since gravitons are spin-2 particles.
This Demonstration closely follows S. Carroll, Spacetime and Geometry: An Introduction to General Relativity, San Francisco: Benjamin Cummings, 2003. The details remain coded with the solution given for geodesic deviation. The solution is in transverse traceless (TT) gauge and represents a wave in the direction, with the particles in the - plane. The test particles are close enough to approximate a locally-flat (Minkowski) metric and are assumed to be non-relativistic () at all times.