this post was submitted on 08 Sep 2023
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It would be roughly the same phenomenon as observing from the ship. Both persons would perceive the other's clock slowing down as the light has increasing difficulty reaching the observer.
You said two different black holes, so there would be time dilation experienced by both when observing the other party. If they were falling together side by side towards the same black hole, their clocks would be basically identical and would experience time in the same way. Even after crossing the horizon, they'd be able to see eachother and interact up until they were spaghettified. This is because light can still move upwards relative to us, and reach our eyes, even if all space is falling faster than light. This was addressed in the video when talking about the local scale of spacetime below the horizon.