c) (10 points) The message transmitted by Mission Control lasts 30 seconds as measured far from the black hole. Do you perceive the message to last for a shorter, longer, or the same duration? What is the name of the relativistic effect involved here? The relationship of the time measured by you, tBH, to that measured at Mission Control far from the black hole, tMC, can be written as: tBH = tMC1/1. - Rs ? (1) = where Rs 2GM/c is the Schwarzschild radius for a Schwarzschild black hole of mass M, and R is the distance from the black hole where you are hovering. d) (10 points) If R = 3Rs and the recorded message is 30s as measured by Mission Control, what do you measure as its duration in seconds? e) (10 points) Say you're short on time and want to hear the full message in only 10s. At what radius R do you need to hover? (Express your answer in terms of Rs)