# Neutron star collapse

Neutron stars are supposed to have an upper limit in mass, beyond which they collapse into perhaps a further type of degenerate matter or a singularity. There doesn't seem to be precisely defined upper limit, but the limit is estimated to be 1.5-3 solar masses. However, a hypothetical neutron star with a mass greater than about 3 solar masses would fit inside its schwarzschild radius, making it a black hole from our perspective.

So why do physicists think that neutron stars collapse any further? It seems like there would be no way of observing whether a black hole is composed of a massive neutron star or a singularity?

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DEvens
Gold Member
The following is all according to general relativity. What happens in quantum gravity we do not know.

If something goes behind its horizon then it cannot do anything except continue to collapse until it reaches a singularity. This is because all time-like paths are inward. That means everything is going to be moving inward no matter what. The details of its content, temperature, etc., will not matter. All motion is inward. Crunch.

The math of that is more complicated than that glib little paragraph makes it appear. But there are quite strong theorems that show this to be the case. Mathematically, going behind the horizon has only one possible result. At least for spherically symmetric systems. I will be carefully vague about non-symmetric systems because I don't understand them.

So the question is, can a given collection of matter support its own gravity well enough to stay outside its horizon? If it can, then it may not collapse. If it can't then it will collapse.

So the question can only be answered based on the details of the behaviour of matter at high temperatures, pressures, and densities. We need to know what the pressure will be that resists gravity in any given situation. We need to know the equation of state, effectively. And that is a complex thing with severe challenges as to measurement. We have to attempt to estimate this behaviour based on physics we can measure. And there are uncertainties.

Example: We can get some basic idea of how matter composed of neutrons, protons, and electrons would behave. At least in a general sort of way. But there are other particles that become important at higher temperatures and densities. Things like baryon resonances start to be produced fast enough by thermal scattering that they become important in the equation of state. Even with their extremely short life times, thermal production will produce enough so that they can act as degrees of freedom in the old 1/2 kT per degree of freedom.

So exactly where a star will collapse and where it will not is difficult to calculate accurately, because we do not have all of the details accurately.

But we know that a large enough mass will be able to go behind its horizon. For example, if you had a galaxy sized mass, the density when it went behind its horizon is comparable to that of air.

phinds