If we can somehow add more matter to a neutron star-- throw another star at it, maybe-- it won't get spatially larger. The extra matter certainly needs somewhere to go. The star must expand. But it doesn't expand in position space. The star expands in momentum space. In position space, it actually gets smaller. The more massive of the neutron star, the smaller its radius. This is a quantum effect, even though it's happening on the scale of a star.
Until now, the neutron star has hovered above a critical size. The space time curvature at the neutron star's surface is pretty extreme. Clocks run noticeably slower. And the densities inside the star produce some very strange states of matter. However, despite this, the star is still very much a thing in this universe. And yet, below the star's surface, there lurks the potential event horizon, the surface of infinite time dilation. Now, the event horizon doesn't actually exist as long as the neutron star stays larger than the would-be horizon.
However, if we can increase the mass of the neutron star, the actual star shrinks, and the event horizon expands. You can see where I'm going with this. There's a mass where the radius of the neutron star and the event horizon overlap. It's three times the mass of the sun. At this point, the event horizon actually comes into being. And the neutron star submerges beneath it. We've finally created our black hole.
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As far as we know, there's no way to overcome Pauli exclusion-- at least, not directly. See, it's not a matter of force. Two fermions just can't ever occupy the same quantum state. And that's that. So the neutron star is safe. Fortunately, there's another quantum phenomenon that lets us get around the Pauli exclusion principle. The Heisenberg uncertainty principle tells us that the properties of a quantum entity are fundamentally uncertain. Quantum mechanics describes matter as a distribution of possibilities. Certain numerical properties that you can assign to a particle exist in a wave varying degrees of maybe. Location is one such property. A neutron, for instance, is not in any one place but exists as a cloud of possible locations that might be tightly constrained or may be very spread out. Location remains a possibility cloud until the neutron interacts with another particle, at which point, its location is resolved. This is the weirdest, coolest aspect of quantum mechanics.
The Heisenberg uncertainty principle tells us that particular pairs of quantities, position and momentum or time and energy, must, when taken together, contain a minimum degree of uncertainty.
If one is tightly constrained, then the other must be uncertain and span a wide range of potential values.So a neutron star is comprised of the densest matter in the universe. Its constituent neutrons are about as constrained in position as you can get. Therefore, the Heisenberg uncertainty principle tells us that they must have highly undefined momenta. Very, very large neutron velocities become part of the possibility space. To put it another way, the neutrons are packed so close together in position space that their momentum space becomes gigantic. Phase space expands. And here's the thing-- the denser the neutron star becomes, the more momentum space you get. So Heisenberg lets us circumvent that pesky degeneracy pressure.
To understand how space works for a quantum object like this, we need to think not in regular 3D space or even 4D space time but, rather, in 6-dimensional quantum phase space. For a neutron star, this is the space of both 3D position and 3D momentum. And it defines the volume that can be occupied by the strange matter in a neutron star. Now, the exact way that the matter of a neutron star fills this 6D quantum phase space depends on two important principles of quantum theory: the Pauli exclusion Power Exclusion Principle principle and the Heisenberg uncertainty principle. These govern the delicate balance between stability and collapse. The Pauli exclusion principle basically just says that two things can't occupy the same place at the same time. And by thing, I mean fermion, the particle type comprising all regular matter. For example, electrons, protons, and neutrons. Now, by place, I mean location in quantum phase space. So two fermions can occupy the same physical location just fine, as long as their momenta or any other quantum property is different. Now, this rule is what keeps electrons in their separate stable orbits and, in turn, is part of what allows solid matter to have its structure.
In the case of a neutron star, position momentum phase space is completely full of neutrons. Every spatial location and every momentum location connected to those spatial locations contains a neutron.
This weird state of matter where phase space is completely full-- we call it degenerate matter. And the degeneracy pressure, resulting from particles not having anywhere else to collapse into, is incredibly strong-- strong enough to initially resist the insane gravitational crush of a neutron star.
Black holes are one of the strangest objects in our universe. To make one, we need both general relativity and quantum mechanics. they are general relativistic entities, as space time regions whose boundary curvature effectively removes the interior from our observable universe.
First step-- find a very massive star, and wait. Let it cook-- not for long because these guys have very short lives. Just wait a few million years for the supernova. If you get impatient, you can turn up the core temperature by bombarding it with gravitational waves. It'll be done quicker.
The details of the deaths of massive stars are pretty awesome. But they can be found in lots of places. So we'll just gloss over them here. In the last throes of a very massive star's life, increasingly frantic fusion in the interior produces one periodic table element after another, in Russian doll shells of increasingly heavy nuclei that finally surround an iron core.
The formation of that core represents the end of exothermic fusion. Fusing two iron nuclei absorbs energy. It doesn't release it. So starved of an energy source, the stellar core collapses on itself. Electrons are slammed into protons in the iron nuclei, forging a neutron star. The collapsing outer shells ricochet off this impossibly dense nugget in a supernova explosion, enriching the galaxy with juicy new elements.
The leftover core, the neutron star, Neutron Star is a very weird beast-- a ball of neutrons the size of a city, with a mass of at least 1.4 suns and the density of an atomic nucleus. We see them, when we see them, as pulsars. Now, beneath the thin atmosphere of iron plasma, a neutron star is a quantum mechanical entity. And it's a quantum phenomenon that saves it, for the moment, from final collapse. It's also a different quantum phenomenon that will let us push it over the edge, creating a black hole.
thanks anon I love this stuff
