[im3w1l]

This might be a stupid question but to me it's hard to grasp that they travel at a "speed" when they are themselves distortions of time/space. Does it always make sense to say they move at the speed of light or only for say small amplitude waves where we can do some quasi-special-relativity trick?

[raattgift]

It's definitely not a stupid question!

Gravitational waves are usually studied in the context of linearized gravity <https://en.wikipedia.org/wiki/Linearized_gravity> rather than the full theory of General Relativity.

Essentially one fixes some background metric that does not have the dynamical aspects of the inspiralling binary. Those dynamical aspects are then applied as perturbations of the background metric. When one then slices the 4-dimensional static background into 3 spacelike dimensions along some timeline, the departures from the background (the perturbations) then propagate like massless waves.

Masslessness (and no refraction, birefringence, etc.) is why the wave propagates at "c".

Light propagates as massless waves too, which is why the speed of light is "c". The constant is geometrical in origin (it's because our spacetime is 4-dimensional, with one dimension of time: gory details at <https://en.wikipedia.org/wiki/Causal_structure>, particularly the "Curves" subsection of the Introduction), although "c" was discovered by studying the speed of light.

Linearized gravity is a good approximation but not fully general. It breaks down in extremes of compactness, and so one resorts to numerical relativity (on supercomputers) for understanding the final parts of inspirals of merging black hole and neutron star binaries (both species are compact, and in the final inspiral each binary partner orbits within the "compactnes-really-matters" region of the other).

[gus_massa]

It's an interesting question. I must take that General Relativity course some day. Meanwhile, I have to guess ...

I guess you are correct and with small amplitudes the apparent speed is equal to the speed of light. For big amplitudes, I'm not sure.

[raattgift]

Pp-wave spacetimes (pp = plane-fronted and parallel) can with suitable separations can have arbitrary constant wave amplitudes. Such spacetimes admit a Killing vector field letting us have a sensible way of measuring the propagation speed of the wave. At any point where it is measured, the propagation is lightlike.

Parts of a spacetime around an equal-mass circular-orbit binary will be reasonably approximated by a pp-wave spacetime (edge-on, not too close to the sources, and over a duration where their orbit is negligibly contracting).