Hi!

It is said that it took Einstein ten years before he discovered the way the gravitation worked (since he had to find a way that did not transport gravitation faster than the speed of light he began a search for it). When he eventually found the answer, it was that gravitation was like waves moving through the universe. He also proved that the gravitational waves had to have the exact same speed as the speed of light. How did he prove that? How did he even prove that gravitation is waves? Is it like longitudinal waves or transverse waves? And is it a kind of electromagnetic radiation with a certain wavelength (the waves would then have to have to have a momentum pointed in the opposite direction to that of the wave in order preserve the law of momentum)? How do these waves in that case really work on the objects they're affecting?