- #36
PeterDonis
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sevenperforce said:If there is a particular event at r=0r=0r = 0 such that an outgoing light signal emitted from that event would intersect the surface of the collapsing core just at the Schwarzschild radius corresponding to the mass of the core, then you have a core-mass black hole already inside the collapsing neutron star.
Yes, you do. But it wasn't sitting there all the time at the neutron star's Schwarzschild radius. It formed as a part of the collapse process, started at zero radius, and gradually increased to the Schwarzschild radius. And if the rest of the star is going to collapse as well, then the hole won't stay at the Schwarzschild radius of the core; it will keep expanding until all the matter has fallen inside the Schwarzschild radius for the whole star. In other words, yes, while the collapse is happening, you will be able to look at it as a black hole being inside a collapsing star; but it won't be a static black hole inside a collapsing star. So you can't use intuitions that are only valid for static holes, for example about "accretion of matter". Matter is collapsing, and during the collapse more and more matter is inside the growing horizon, but this process is different from the process of accretion of matter onto a hole that has been sitting there static for a long time, surrounded by vacuum, and then suddenly has a large amount of matter fall into it.
A key thing to keep in mind here is that the definition of the event horizon is inherently "teleological"; that is, it depends on what is going to happen in the future. In other words, there is no way to tell locally where the horizon is; to know where it is, you have to know the entire future of the spacetime. So your normal intuitions about objects don't work; you can't think of the horizon as something that is forming because of what already happened. It is forming because of what is going to happen--because all the matter is going to collapse inside the Schwarzschild radius corresponding to its mass. So you can't have a scenario where only part of the matter falls in and then you have a static hole, because if only part of the matter falls in, either the horizon won't form at all, or it won't stay static (as above).
sevenperforce said:trying to derive the minimum mass by looking at where the math would no longer make sense
We already know at least a heuristic answer to this: the minimum mass is the Planck mass. There is nothing in the math that shows any problem for any hole larger than that, at least as we understand it today.