The conversation between human and AI assistant.
Why do gravitational waves only stretch and strain space in the transverse direction?
Why is that, though? Why don't gravitational waves cause stretching and compression in all directions?
This happens because the intrinsic geometry of spacetime has a definite curvature that responds only to transverse or sideways deformations caused by gravitational waves. In essence, the curvature of spacetime will only change due to changes in the transverse direction, and not in the direction of wave propagation.