If a particle was dropped into the sun’s gravity (not with “horizontal” motion that might cause it to orbit), is it time dilation that causes it to accelerate toward the sun somehow?
My guess: In the reference frame where the particle is not moving, the sun would be either a) moving (with a perpendicular component) and be ever so slightly moving toward the particle or b) not moving but a third body would be, moving both the sun and the particle at different “strengths” (different mass and distance, different time dilation) thus the particle and the sun would appear to move closer to each other. That means in either case (sun in the middle or particle in the middle) the third body moving closer must make it look like the particle and sun are gravitationally pulling each other. If we then shift reference frame back to the third body being stationary and the particle and sun moving, we should see that. It would be really cool if we could simulate this to test it but I believe that would require solving the 3 body problem.