What happens to objects falling to a black hole (from outside observer's perspective)?

There seem to be a consensus that because of time dilation, an object's fall towards event horizon will take a long, ever-stretching time. There seem to be no consensus regarding whether this fall will take finite or infinite amount of time, or, because the object will cease to be observable, the whole question is moot.

Consider the following scenario: There is a Schwarzschild black hole of 10 solar masses (event horizon radius of 29.5 km), and there is an object falling to it, which is close to the event horizon, nearly frozen because of time dilation, but the one that we STILL CAN observe. The black hole is growing over time from 10 to 20 solar masses, which causes its event horizon to increase to 59 km. What will happen to the falling object, from outside observer's perspective?

  1. The object will cross the event horizon, and there can be some proof of it;

  2. The object will cross the event horizon, but there never can be any proof;

  3. The object would get "plastered" over the event horizon and pushed outside as it expands.

There is a number of questions here on physics SE discussing black hole origination and falling into it, but does not seem like any which discusses this particular scenario.

  • $\begingroup$ If I'm going to be a smart aleck about this, the event horizon of an expanding black hole lies strictly outside of the "you have to travel at the speed of light to move radially outward" sphere during the time when the black hole is expanding, so the object DEFINITELY crosses that region for any observer. $\endgroup$ Mar 6, 2020 at 21:39
  • $\begingroup$ The object will remain exactly where it is and the horizon radius will expand $\endgroup$
    – Wookie
    Mar 6, 2020 at 22:38
  • $\begingroup$ Because of the diverging time dilation, there is no relative movement at the horizon. Anything at the horizon is locked to the horizon and moves with it wherever the horizon moves. This is called Linear Frame Dragging. Related or duplicates: Does an expanding event horizon “swallow” nearby objects? and How can anything ever fall into a black hole as seen from an outside observer? (see the accepted answers posted by Anixx). $\endgroup$
    – safesphere
    Mar 7, 2020 at 6:56
  • $\begingroup$ @JerrySchirmer You comment is incorrect for the following reason. When an object $m$ approaches a black hole $M$, the event horizon expands toward the falling object while the object is outside. This is well known and proven by numeric modeling. By the time they meet, the horizon expands to $2(M+m)$. So a black hole grows without "swallowing" matter. Nothing moves relative to the horizon, because of the linear frame dragging due to the infinite time dilation. In the view of any external observer, nothing crosses the horizon ever, no matter how the horizon moves. $\endgroup$
    – safesphere
    Mar 7, 2020 at 7:12
  • $\begingroup$ @safesphere: simple constructs allow you to be outside the apparent horizon but inside the event horizon in flat spacetime in the case of expanding horizons. You can cross from one region to another wihtout ever crossing a region of infinite time dilation. There are numerous examples of this in both MTW and in a relativists toolkit. See also the Ashtekar and Krishnan work on dynamical horizons. $\endgroup$ Mar 7, 2020 at 16:54


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