Answer:
equivalence principle. Particles follow geodesics that are extremal paths in spacetime. These paths are the same for any mass m so long as this test mass is small m << M for M the mass of a central mass that defines a gravity field. If the spacetime curvature is due to a gravity wave or some other physics, the curvature of this field R is such that R >> 8πGm^2. If this test mass is sufficiently large it has its own appreciable curvature and this results in a highly complex problem similar to the 3-body problem in Newtonian mechanics.
I have though been thinking about this a bit differently. The equivalence principle states that the freely falling frame is equivalent to a frame in flat spacetime far removed from any gravity field. I have been thinking of this according to quantum field theory. A freely falling frame is one which has a vacuum equivalent to a quantum vacuum in flat spacetime. The geodesic the frame falls under is one which preserves this vacuum.
This may be extended to massive particles and massless particles. A massless particle is on a null geodesic and is then on a “null frame.” These frames are then projective varieties over massless quantum fields in that vacuum. These massless fields all have transverse modes, but no longitudinal modes. A massive particle has a longitudinal mode, and the vacuum modes have dispersion as a result. This is due to the presence of the Higgs field.
An accelerated frame is one which has a vacuum equivalent to a particular vacuum near a black hole. Depending on the acceleration parameter this can be a different vacuum. In this way aspects of spacetime physics can be thought according to quantum mechanical or quantum field properties. Spacetime is probably an emergent phenomenon of quantum physics.
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