I have a question of the constant of the speed of light. I understand that the speed of light is a constant and the faster you accelerate, you'll still experience light traveling at that same speed because time itself slows down for you. Gravity also distorts spacetime and causes time to slow down.
My question is, if two stars that are an equal distance away each released a photon at the same time towards Earth, and there is a massive gravity well in the path of one of the photons, would they arrive at the same time? Light travels at approximately 300,000 k/s, but in the gravity well, a second is a different length than in empty space. Shouldn't it take longer for that photon to arrive?