Collision of massive black holes at the speed of light

Question

The time slows down due to two reasons: $1.$ high speed, $2.$ high mass relative to the radius.

Basically, assuming that we are living on a black hole, we will very very slowly get older compared to the others. On the other hand if we travel at near speed of light, then again time will slow down relative to the other things around.

Then a natural question is what happens when both happens relative to the case when a single one of them happens? will a person on a black hole traveling at a near speed of light gets slowly older compared to the one just sitting on a slowly moving black hole?

What would happen if these two massive black holes would collide at a speed of light? I know that black holes are not traveling at the speed of light and probably it is impossible physically but theoretically it is possible. What would be the effects of such a collusion? I mean would the whole universe be affected? would there be new particles which was never known before?

I am aware that there will be time dilation for both cases (like black hole at the speed of light and black hole slowly moving). I have the formulas: $\sqrt{1-v^2/c^2}$ and $\sqrt{1-GM/Rc^2}$ and if any of them goes to zero, then we are basically done. when both of them tends to $0$, I am trying to understand the difference.. Here the observer is the person who is not near any massive object and not moving.

Questions:

1- If there is a person on earth, and one traveling at the speed of light, then the person taveling at the speed of light wont be aging at all with respect to the person on earth. If another person is traveling at the speed of light on a massive blackhole, then this person wont be aging too. What is the difference in both cases? it seems in both cases the person traveling at the speed of light are immortal. so what is the difference of being on the black hole?

2- If two massive black holes collide at the speed of light. what are the predictions of Physics? Will it destroy the universe? Will there be new particles? can such a collusion create dark matter or dark energy?

Answer 1

The time dilations are relative from your frame with an observer.

Gedankenexperiment: start with two black holes of equal mass with identical clocks. Accelerate the second black hole to 0.999 c. The clock on the stationary black hole will seem to go faster than the speeding black hole.

Answer 2

1) Yes, other things being equal the person travelling near (not "on") a rapidly moving black hole should have more time dilation than the person near the slowly moving black hole.

2) Any collision of large black holes is likely to generate a whole lot of gravitational radiation. You would not want to be anywhere near it. And in fact when black holes do collide they will be moving at a significant fraction of the speed of light, because much of the potential energy from their initial separation (basically everything that hasn't already been radiated away as gravitational radiation) will have gone into kinetic energy.