An astronaut is travelling towards a black hole in a space ship traveling at 0.8 C. The guy’s position is not fixed relative to the black hole. He is travelling towards it from a distance. How to calculate the gravitational time dilation in this case, as the "relative time" keeps getting slower as one approaches the event horizon?
Please note that I have already factored the ‘time dilation’ due to the space ship traveling at 0.8 C. I just want to understand the ‘gravitational time dilation ‘ part of it.
Can some form of integration be applied on the gravitational time dilation equation for the case of motion in gravitational field?