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I understand the time dilation around a black hole to imply that when an object touches the event horizon of a black hole, the signals sent from the object will take infinite time to reach an observer.

I also assume that this effect would prevail for an observer not only at infinite distance to the hole but for any observer further away from the black hole than the object touching the event horizon.

If this is true I wonder about the time dilation effects discussed in a number of posts relating to a black hole interacting with Earth.

The collision with the black hole would occur at some point, but if the neighboring masses of earth never would “see” (i.e. experience) any passage through the event horizon for the masses located at the impact I would expect that to have some effect on the description of the collision.

Is this not a complication in these hypothetical scenarios?

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You are asking about two things:

  1. from the viewpoint of Earth itself

As an observer passes the event horizon, the observer experiences nothing special (except for spaghettification). In reality, the observer might not even realize he passed the event horizon.

If you disregard the effects of extreme curvature (on the different parts of Earth, and on its rotation), then the Earth would just pass the EH and nobody on Earth would notice nothing special (OK, the Sun and anything else on the sky would disappear).

In reality, if Earth would collide with a BH, the first thing to be pulled towards the EH is the atmosphere, then the liquid parts, oceans, then because of the extreme curvature, even the shape of Earth would become spaghettified.

  1. from the viewpoint of a far away observer, away from Earth. In this case, the observer would just see the Earth frozen on the EH forever, because of GR time dilation.

You might be asking something different. If you are asking about two different observers on different parts of the Earth, then this could be interpreted as two co-moving observers.

In this case, two co-moving infalling observers would experience the switch between the time dimension and the spatial dimension (pointing towards the singularity). Time would just be the dimension that leads towards the singularity, and the spatial dimensions would take the interpretation of time.

After your comment, you are asking about what happens when there are two people standing on different parts of Earth. One observer already passes the EH, while the other not yet. The observer who did not yet cross, will see the other one frozen on the EH.

But this time while the observer sees the other one frozen is not infinite. Why? Because the observer who sees the other one frozen on the EH is moving towards the horizon too, and will reach it in a finite time. At that point, both have reached the EH, and will be inside of it. From there, they will be regarded as two comoving infalling observers.

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  • $\begingroup$ I am thinking of the effect on the adjacent masses. For example, the first molecule in the atmosphere would never be seen to be entering the event horizon, EH, by its neighbor molecule because of the difference in distance to the EH. Similarly, the first mass of rock impacted would not be seen to enter the EH either by neighboring masses of rock etc. If nobody sees any material leave it seems to counter to the scenario where the whole planet disappears. $\endgroup$ – Mikael Jensen Jul 15 at 13:38
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    $\begingroup$ @MikaelJensen OK I will edit my question. You are asking what happens in the meantime while one person on Earth sees another person on another part of the Earth already pass the Horizon. Yes you are right, there would be a certain time while the observer would see the other one frozen on the EH. But this time in this case is not infinite, since the other observer is moving towards the EH too in a finite time they will both reach the EH. $\endgroup$ – Árpád Szendrei Jul 15 at 13:43

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