[da-bacon]

"but the physics of it is relatively straightforward."

Amusingly Einstein both identified gravitational waves in his then new general relativity and then changed his mind about whether they existed. Indeed he had found three different types of these waves, and two of them were simply coordinate artifacts (they could be made to travel at any speed, Eddington famously quiped that they could be made to move at the "speed of thought"). The third type however didn't have this problem (though again here Einstein would write a paper where he claimed these gravitation waves required singularities, but these turned out these were all coordinates singularities .... sort of like how late and long coordinates misbehave at the poles)

In some ways the physics of it is straightforward, in other ways....not so much.