What Determines the Speed of Gravitational Waves?

[jtbell]

Local quantities are perfectly legitimate.

Sure. But you have to measure them locally. That is, you have to be at the location in question. If you measure them "remotely", from some other location, you have to take into account the spacetime curvature between the two locations.

 

[tom.stoer]

I am saying the following: Two observers A and B in curved spacetime at rest w.r.t each other but located at different spacetime points P_A and P_B will not agree on the velocity of a test body C w.r.t. to e.g. observer A:

v_C(w.r.t. A, measured by A = observed from P_A) != v_C(w.r.t. A, measured by B = observed from P_B)

That means the velocity is no longer globally valid. It does not only depend on the velocity of the two reference frames for A and B (wich is well-known from SR), but also on the location of these reference frames (= tangent-spaces) in spacetime.