Can I move a black hole with the aid of a lever?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.