Ok this is actually interesting now. Let's model this according to velocity effects as opposed to gravitational effects. Bob is watching Alice fall into the black hole. The gravitational effect would be similar to Alice going away from Bob at near c. Her light would redshift and her time would appear slower and slower from Bob's perspective but remain at the normal rate from her perspective. The gravitational effect would manifest itself just like an imbalance in relative velocity with Alice choosing +c away from Bob. Relativity does not allow the calculation of age difference for this scenario but in my math, Alice is ageing faster than Bob even though he sees time has stopped for her and she sees time remains passing normally within her frame.
In the velocity analogy, Alice only ages faster for a time after she makes the jump to near light speed which is analogous to her reaching the event horizon. She will age 2 yrs for every light year separation between the event horizon and Bob's distance from it. Of course, in the velocity analogy, the total faster ageing time for Alice is dependent on light being able to reach Bob from when she jumps to light speed which can't happen from the event horizon. Also, she's accelerating the entire way to the event horizon and it's not like she's making just one velocity change as she would in the velocity analogy so I don't know what the answer is. However, if she jumped to near +c at some distance from Bob and the event horizon towards the event horizon, she is effectively bringing that event horizon outside the black hole to a point where a light signal will reach Bob. So she will age 2 years for every ly separation from Bob when she makes the jump to near +c until the signal reaches Bob that she has made the jump. After that, they continue ageing at the same normal rate even once she reaches the event horizon. This is as close as I can come to an answer with the tools I have. I can't make a call on what happens if she just falls towards the black hole at the acceleration due to gravity.
What conclusion can you come to with your relativistic math instead of your fingers to the wind.
PS. So I can effectively take the black hole out of the equation and reduce the problem to one of linearizing an average velocity of Alice's fall towards the event horizon from a co-located starting point between Bob and Alice and adding a point where Alice makes a jump to near +c that is consistent with the average velocity of the fall to the event horizon. The time for light to travel back to Bob from that transition point would establish how long Alice would age at 2c which would give a total time Alice has aged more than Bob once she hits the event horizon at c and blows up the entire universe in the process.
PPS. What happens after the transition doesn't matter in either case. Whether it's a black hole blocking anymore light reaching Bob or Alice's near light speed causing subsequent light from not reaching Bob, the effects are the same on Bob's perspective reality of Alice. Well, there's your answer. If the event horizon acts in essentially the same way as Alice's jump to +c, I can linearize the average velocity of her fall to the event horizon from her starting point with Bob and she will age 2yrs more than Bob for every light year her starting point is away from the event horizon. She will only begin to age faster once she hits the event horizon and will stop ageing faster once the distance between her and Bob could have been covered by a virtual light signal. Let;s say the distance was 3 light years, she'd age 2 yrs per light year for a total of 6 yrs older than Bob forevermore.
Edited by ralfcis, 25 March 2019 - 04:43 PM.