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Since Sept 2019 there's been some speculation1 whether the hypothetical planet far beyond the Kuiper belt is actually a primordial black hole. It would be the closest black hole to the Earth (500 au from the Sun on average) and we might send a probe there.

I've already discussed the speed needed to enter the black hole on astronomy.SE and a user (don't remember who anymore) concluded that the probe must enter at close-to-light-speed in order to not get spaghettified and torn apart. And since the black hole would have a diameter of about 2 inches (5 cm) the probe must be very small of course, with the camera on its peak, so that it enters the black hole camera-first. The probe probably would consist only of a camera.

Is it realistically possible to achieve a speed of 0.95 c for a probe (perhaps Breakthrough Starshot with a swing-by on a star) and what else would it take to make the probe safely fly into the black hole? And might it be risky because a man-made probe might exit the black hole in another location and/or time?

Perhaps I should tell you that it doesn't matter whether the speculation is true. The question is what it takes to enter it, so just assume there is a primordial black hole.

1Gizomodo's What If Planet Nine Is a Bowling Ball-Size Black Hole? links to the arXiv preprint What if Planet 9 is a Primordial Black Hole?

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    $\begingroup$ "Safely" and "black hole" can't be used in the same sentence. $\endgroup$ – GdD Apr 16 at 7:32
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    $\begingroup$ I love the image of the "Exact scale (1:1) illustration of a 5M⊕ PBH" :-) $\endgroup$ – uhoh Apr 16 at 7:53
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    $\begingroup$ @uhoh But I think that depends on how much zoom you use in your browser. $\endgroup$ – user35272 Apr 16 at 7:55
  • $\begingroup$ For Gizmodo that's certainly true, but for the PDF in the arXiv paper I think those files contain real dimensions in their embedded images. I'm no expert on it, but I think if we printed out the PDFs anywhere in the world with different paper standards 8.5x11 vs A4 we'd get almost (if not exactly) the same size. $\endgroup$ – uhoh Apr 16 at 7:59
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    $\begingroup$ It doesn't matter how fast your probe goes. It can't outrace the event horizon's gravitational time dilation, gravitational redshift, and the fact that it's an event horizon..No information from any part of the probe that crosses the event horizon in its own reference frame gets back to any reference frame that isn't also crossing the event horizon. $\endgroup$ – notovny Apr 16 at 10:34
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the probe must be very small of course, with the camera on its peak, so that it enters the black hole camera-first. The probe probably would consist only of a camera.

What would you hope to accomplish by that? Information can not escape the event horizon of a black hole. That's why they are black. If you could "dip" a camera behind the event horizon (which you can't, because it won't be a functional camera at that point), the image it records could not pass back outside. The image signal would have to travel faster than the speed of light in order to escape the event horizon, which is impossible according to our current understanding of physics.

Is it realistically possible to achieve a speed of 0.95 c for a probe (perhaps Breakthrough Starshot with a swing-by on a star)

No, not with present technology and likely not with foreseeable future technology either. The fastest speed for a space probe I could find is NASA's Juno probe with 692,000 km/h. That's 0.00064c. And the problem with relativistic speeds is that the closer you get to the speed of light, the more energy you need to accelerate further.

There is also the question what you would want to accomplish by doing that. You will only get a very, very short time window in which the probe could collect any data. In order to maximize scientific value you would want the probe to observe the object for a longer time. Even if you would want to observe the probe from the outside while it gets swallowed by a black hole, you would want that to happen slowly so you can collect more data.

and what else would it take to make the probe safely fly into the black hole?

You can not "safely" fly into a black hole. You might get some interesting data by flying a probe near a black hole. But you can't get it too close to a black hole, because the gravitational shear forces will tear it apart.

And might it be risky because a man-made probe might exit the black hole in another location and/or time?

  1. There is no scientific reason to believe that black holes can do that. That's something science fiction authors made up. The current consensus among astrophysicists is that anything that falls into a black hole becomes a part of it and is irretrieveable lost. Any information about what it once was is lost. It just contributes to the hole's mass, electric charge and momentum.
  2. Even if the scientists thought wrong and the science fiction authors guessed right, the gravitational forces would crush the probe into worthless bits of scrap metal long before it touches the event horizon.
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  • $\begingroup$ White holes are one theory. If you enter a black hole and reach where "singularity" is presumed, you can in fact exit the black hole in a white hole on the other side. There's a report of a pilot (don't remember his name) who above the Bermuda triangle flew through an Einstein Rosen Bridge which teleported him to his goal Miami. It looked like a tunnel within a strange cloud. The extreme magnetism there might explain the opening of such bridge. $\endgroup$ – user35272 Apr 16 at 10:53
  • $\begingroup$ I found out the pilot's name: Bruce Gernon Jr.. He reports to have flown through a ~1 mile tunnel where he was weightless and the instruments of his airplane failed until he exited the Einstein Rosen Bridge. $\endgroup$ – user35272 Apr 16 at 11:17
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    $\begingroup$ @user30007 There is so much about that story which makes no scientific sense whatsoever that I can not explain it within just 600 characters. You might want to post that story on skeptics.stackexchange.com and let them point out all the flaws in that story. $\endgroup$ – Philipp Apr 16 at 11:19
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    $\begingroup$ @user30007 "Obviously flew to other planets"? Uhmm.... no, there is nothing obvious about that. You really should stop believing everything you read on paranormal mystery websites or see on History Channel. $\endgroup$ – Philipp Apr 16 at 12:01
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    $\begingroup$ @user30007 Ummm..no. They pretty much fly all over the Bermuda triangle. Pilots don't actively avoid it. $\endgroup$ – Star Man Apr 18 at 15:02

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