I'm basically duplicating this question, because I'm not satisfied with the answer.
Here's why I'm not satisfied.
If we know that "gravity travels at a finite speed", then it seems obvious that it can cause waves.
You don't need to be a genius like Einstein to figure that out. Sure, you might not be able to write down the equations that model its behavior as Einstein did for general relativity, but the mere prediction of the existence of gravitational waves hardly seems surprising (in fact, seems necessary) when you've already considered the idea that nothing can travel faster than light.
Now, I don't know who first had the idea that gravity might travel at the speed of light, but it sure doesn't seem to have been Einstein. (Wikipedia says Poincaré argued for this idea in 1904?)
Considering these, why do we say Einstein predicated the existence of gravitational waves, and why does it seem like such an extraordinary conclusion? Doesn't it seem like a trivial corrolary of the fact that gravity has finite speed, which had already been experimentally verified? Why were the recent discoveries such a big deal, and why does Einstein get all the credit for it?
Or, is it the case that, e.g., the waves predicted by Einstein somehow behave fundamentally differently from what you would expect from a finite-speed Newtonian gravitational wave?
Am I missing something there?