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Suppose you want to mine material from, and eventually completely disassemble, a neutron star. Presumably, you would be extracting heavy elements from the crust, and expecting the neutron-degenerate matter underneath to decompress and undergo beta-decay, turning back into more normal heavy elements as you go. Perhaps you need the material to build trillions of space habitats, or a few hundred spare rocky planets or something.

What would be the easiest, most plausible means of accomplishing this using foreseeable technology? It is permissible to assume any necessary conditions on the particular star's characteristic or pre-existing environment, such as that the neutron star must be part of a binary system with a specific other object, or that it must have pre-existing planets, but fewer and weaker preconditions are of course better.

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    $\begingroup$ You have tagged this question "hard-science." That means you're asking for scientific citations, detailed calculations and the like. Do you really mean "science-based", in that you want an answer that is as scientifically plausible as possible? $\endgroup$ – John Dallman Sep 9 '17 at 21:40
  • $\begingroup$ @JohnDallman Detailed calculations & citations would indeed be appreciated. $\endgroup$ – Logan R. Kearsley Sep 9 '17 at 22:00
  • $\begingroup$ I am a bit confused by the combination of terms "foreseeable technology" and "neutron star mining" in a post with a "Hard-Science" tag. I'm pretty sure we're solidly in the realm of talking about hypothetical systems, not plausible systems. Any explanation would likely need to involve something like negative mass systems or devices capable of moving solar systems worth of mass to relativistic speeds. Hypothetically, sure. Plausible future technology - no. $\endgroup$ – GrinningX Sep 9 '17 at 22:23
  • $\begingroup$ @GrinningX Could you use a (much smaller than a solar system!) relativistic impactor to blast off more mass than is in the impactor itself? Could you use a Nicoll-Dyson swarm around a nearby companion star to evaporate or blast off material, or to spin the NS up (per Swier's answer) with differential light pressure until it breaks up? I don't know, hence the question, but if they were to work all of those would be foreseeable technology, in that they do not require any new physics-just a lot of resources and engineering-and calculations can be done to validate their physical plausibility. $\endgroup$ – Logan R. Kearsley Sep 9 '17 at 22:44
  • $\begingroup$ Considering the wording in your question, it seems you're not actually interested in the neutronium, just the iron and whatnot in the crust. Is this reading correct? $\endgroup$ – No Name Sep 9 '17 at 23:52
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Dealing with Neutronium has some rather startling consequences, such as it being a massive explosive when released from the immense gravitational pressure holding it together. In addition the environment around neutron stars is pretty dramatic. There are immense magnetic fields, beams of charged particles coming from the magnetic poles and tidal forces due to the immense gravitational field concentrated in a very small area which would stretch you out like a piece of spaghetti.

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Schematic of the magnetic field and particle beams surrounding a neutron star

So setting down your lunch box and punching into the worksite at the Neutronium mine is going to be rather challenging.

Since the neutronium is both held together and stabilized by the intense gravitational field of the neutron star, you will need to counter the gravitational pull of the star, yet somehow keep the neutronium compressed in a usable fashion. Sadly the best way of destroying a star to retrieve bulk elements from the core is to detonate a type 2 Supernova, but that requires the nuclear fusion reactions in the star to run up the curve of binding energy from Hydrogen to Iron. Once there is no longer any fusion energy from the core (Iron neither releases energy from fusion or from fissioning) the remainder of the star collapses from gravitational pressure and the core implodes. The neutron star might be the remnant of the Supernova event, so there is no energy available to break the star apart.

This means external energy must be applied, and since the gravitational energy of a star is so immense, the energy required to overcome this must be at least equal to the gravitational binding energy, and ideally greater in order to allow the material to be flung free of the worksite. The only plausible way would be to crash another neutron star into the mined star at a high velocity, or to bring the neutron star close enough to a black hole to have the gravitational energy of the black hole rip the neutron star apart, where the neutronium then spirals into the accretion disc. (How you retrieve the neutronium from there is an exercise for the reader....)

The other problem really has no solution with known or plausible physics. The Neutronium will decay because there is no strong nuclear force to bind them together and the gravitational energy that kept them bound and stable has been removed. The Neutrons will rapidly decay as per the initial link, and there will be a blaze of energy as the neutrons are converted into a proton and electron:

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Neutron decay

So perhaps the best advice to the would be industrialist is to leave sleeping neutron stars lie...

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Neutron stars are much too extreme for any form of matter consisting of multiple atoms to get close and live to tell. So conventional mining is out.

This leaves us with somehow breaking a neutron star up from far away, which is actually more plausible than you'd expect:
If you find a neutron star that's spinning extremely fast, you could feed it a lot of mass. This would further increase its angular velocity. If the spin reaches around 1500 revolutions per second, it is predicted that the neutron star will break apart.
It is also predicted that neutron stars with this much spin will lose their angular momentum to gravitational waves faster than they gain through accretion. But as you're probably breaking the neutron star apart quite fast (i.e. not cosmological time scales), this shouldn't be an issue.

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    $\begingroup$ The "hard-science" tag gets taken very seriously. Can you back up what you're saying with mathematics or attributed empirical evidence? $\endgroup$ – JBH Sep 9 '17 at 23:14
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There's no known technology to do it, thus I'm going to have to weasel a bit on the hard science tag. For what I have in mind you will need some sort of gravity projector:

1) Spin the neutron star up as much as practical.

2) Use your gravity projector to lift a bit of material from the equator.

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