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Assuming I had an intergalactic lever and fulcrum that was long and strong enough to engage with a black hole, could I move the black hole? What would happen to the end of the lever as it approached the black holes?

Níckolas Alves
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Kenn Magnum
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    Fascinating question. The time dilation at the black hole is going to play a major part in this answer. I would think that the lever would sweep past the event Horizon. After that point matter breaks down. So I don't think it could have an impact on the singularity, if indeed there is a singularity. – foolishmuse Oct 28 '22 at 01:36
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    I also found a similar question with other ways to move a black hole. https://physics.stackexchange.com/questions/235816/is-there-a-way-to-move-a-black-hole – Wippo Oct 28 '22 at 02:22
  • @safesphere Can you expand on that. Make it a full answer. – foolishmuse Oct 28 '22 at 15:23
  • @safesphere Great response. Let's see; when a truck passes a road sign, the wind from the truck rattles the road sign. If we put in a larger road sign, does it actually effect the movement of the truck? In the OP, would the lever simply get blow by the frame dragging? Or by impacting on the space around the black hole, would it move the black hole? – foolishmuse Oct 28 '22 at 18:24
  • @safesphere excellent analogy. You should write this up as an answer and get major points. Your interpretation is completely different from anything else posted. – foolishmuse Oct 28 '22 at 21:43
  • The very idea of a 'lever' requires body rigidity, but there is no such notion in general relativity. See for example https://physics.stackexchange.com/q/48392/109928. – Stéphane Rollandin Oct 30 '22 at 10:04

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Preface: I'm not a physicist nor an astronomer so take my answer as a mere opinion.

I don't think it's possible to move a black hole by pushing it, if that's what you mean. I can't think of any way you can push something that has such a force that even light cannot escape. The portion of the lever in contact with the hole would be disintegrated.

To me, a more realistic way to move a black hole would be to use gravity. You just need an object with enough mass to attract the hole to itself.

Buzz
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Wippo
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    Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. – Community Oct 28 '22 at 02:00
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As other answerers have pointed out, one way you could use a lever to move a black hole is to use the gravitational attraction of the lever. However, this does not really use the "lever-ness" of the lever.

Another mechanism for moving a black hole is to impart momentum into it by having part of the lever fall into the black hole. (As @g s points out in the comments, if you use the gravitational attraction between the level and the hole to move the hole, you are still conserving momentum of the entire level+fulcrum+black hole system). A version of this occurs in binary black hole mergers; asymmetric generation of gravitational waves from the mereger imparts a "kick" to the remnant black hole. The gravitational waves carry off momentum in one direction preferentially; the final black hole carries an equal and opposite momentum by moving relative to the center of mass frame of the two initial black holes.

Similarly, if you were able to throw a lot of matter/energy into one side of a black hole, you would expect by momentum conservation for the black hole to start moving, after absorbing that matter.

Where the "lever-ness" comes into play here, is that by using a relatively small motion on the short end of the level, you can create relatively larger motion of the long end of the lever. In principle, if you could impart a large momentum to the part of the lever that got swallowed by the black hole, you could use this transfer of momentum to move the black hole.

The devil is in the details, however. To make a solar mass black hole move at, say, $1\ {\rm m\ s^{-1}}$, you would need to impart a momentum of about $2\times 10^{30}\ {\rm kg\ m\ s^{-1}}$, which is about 10 times larger than the momentum of the entire Earth moving in orbit around the sun. Needless to say, you would need quite a large lever to achieve this effect.

Andrew
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    +1 for momentum conservation. I would suggest that this answer could be improved by mentioning that the gravitational attraction approaches are also momentum-conserving collisions if you zoom out far enough to see the whole counterweight-Archimedes-lever-fulcrum-load system. – g s Oct 28 '22 at 19:16
  • @gs Good point, I added a comment. – Andrew Oct 28 '22 at 23:16
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Archimedes is famous for saying "give me a lever long enough and a fulcrum on which to place it, and I shall move the world." The mass of a black hole is simply the mass of the body from which it was formed. So if the Earth was crushed to a black hole (less than 1cm in diameter) in theory you could move it. BUT: the physics around a black hole adds a whole other dimension to this problem - literally. As is mentioned in comments, tidal forces and time dilation (spaghettification) would break apart anything, including an infinitely strong lever, as it approaches the event horizon. Even at the quantum level, particles become stretched and break apart at the horizon. So I don't think it is possible to use a lever in the normal sense to move a black hole.

foolishmuse
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  • The gravity of a black hole is exactly the same as that of any other body of equal mass far away from the event horizon. – FlatterMann Oct 28 '22 at 15:49
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Yes, of course you could. The end of the lever gets attracted by the black hole and the black hole gets attracted by the end of the lever. Hence the black hole moves. You simply never come too close and it's all good. This is not a complicated question and exactly this maneuver has been suggested to deflect asteroids without ever touching them: a spacecraft of large mass would simply hover above the surface at a constant distance and engage a small engine that would slowly change the orbit of both the spacecraft and the asteroid. The max. momentum transfer would be very small, though.

FlatterMann
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    Black hole and asteroids are not the same thing. The tidal effect due to the BH will break apart the hypothetical lever as it gets drawn towards it. The same is definitely not true for asteroids – KP99 Oct 28 '22 at 13:55
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    The original question did not imagine a lever of large mass, sufficient to pull the black hole through gravity itself as would another black hole. We are only dealing with a lever with enough strength that it won't break when used on the mass of the black hole. – foolishmuse Oct 28 '22 at 15:26
  • @KP99 The effects due to gravity are the same for a black hole and any other body of equal mass as long as we are far away from the event horizon. – FlatterMann Oct 28 '22 at 15:27
  • @foolishmuse I don't know what that is supposed to mean. We are already talking about an impossible lever. I am simply assuming that it has some mass and I am staying far enough away from the black hole that it won't break. Now you want to have a super-long, super-strong massless lever in addition? – FlatterMann Oct 28 '22 at 15:29
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    @FlatterMann I believe the original question is thinking of a really long lever and using it in the normal lever/fulcrum sense. He is not thinking of simply using the mass of the lever to move the black hole through gravity; that is a different issue. If he was thinking of that he just could have said would a nearby large planet move a black hole. – foolishmuse Oct 28 '22 at 15:38
  • @foolishmuse I am thinking about the same. If he wanted to ask if one can lower anything below the event horizon, then he should have asked that question. The answer to that is no, but that does not mean that one can't move a black hole. Of course one can and the universe does it all the time. – FlatterMann Oct 28 '22 at 15:41
  • In the standard lever/fulcrum arrangement, it is kind of implied that one has to bring the lever in contact with the BH, which is where the tidal forces become significant. However, you are correct that the any mass can displace the BH in principle – KP99 Oct 28 '22 at 15:45
  • @KP99 In the question the word "engage" is being used. There is nothing about "contact force" in there. At this point you are simply arguing about semantics. Of course gravity "engages" a black hole. If the question was about contact forces, then it should have been more precise. – FlatterMann Oct 28 '22 at 15:48
  • Well, OP should clarify ‍♂️ I thought "engage" means bringing in contact with BH in the usual lever/fulcrum sense – KP99 Oct 28 '22 at 16:00
  • @KP99 What would you make a lever out of that could withstand "contact" with the surface of the sun? – FlatterMann Oct 28 '22 at 16:05
  • Maybe one can consider a hypothetical material which can withstand Sun's surface temperature and durable enough for tidal effect and frame dragging effect near the surface. Here, you can assign a "lower bound" to the strength and durability of lever to push Sun. – KP99 Oct 28 '22 at 16:30
  • @KP99 Maybe we can consider a hypothetical material made out of cosmic strings wrapped in M-branes that can be lowered into black holes? That's not physics. That's magic. – FlatterMann Oct 28 '22 at 20:31
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Yes you can move the black hole, as long your lever does not approach it too closely. Just use the attraction between the mass of the lever and the mass of the black hole. Thus you 'pull' the black hole from above rather than push it from below. (So this is different from how we use a crow-bar.)

To get a bigger force, you could first trying charging the black hole with some electric charge and then you could use the electrical attraction or repulsion from a charge on the end of your lever.

As long as the lever is more than a few of Schwarzschild radii away from the horizon, the physics is quite similar to any other astronomical body.

Andrew Steane
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