Related to: How fast does gravity propagate?
In the related question and in many other questions here, it seems as if the propagation speed of the gravitational interaction is $c$. To my understanding, the only axioms of relativity is that the propagation speed of light (read here EM waves) in vacuum is $c$, and that the laws of physics must be the same in every inertial reference frame.
How can we conclude that the propagation speed of the gravitational interaction is the same as the propagation speed of the EM interaction?
