I would say much of this is unknown. Even the minimum mass of BH you would get by incrementally growing a neutron star is unknown (3 to 5 solar masses is an estimate, but that is an error bar of a whole sun). Qualititatively, all agree (including my hypothetical adding iron to a neutron star), that the final collapse to a BH would be sudden.
I don't know of any real analysis of a model of incremental BH formation from a neutron star (it would be a lot of work, and since it isn't known to occur, maybe no one has been motivated). Or maybe I've missed it in the literature. So I really can't answer the 'how fast' question with any confidence. It may not make much difference because the speed of sound would be a significant fraction of the speed of light for a neutron star (e.g. > .3 c).
What do you mean by spacetime free solutions? Since SR and GR are built on spacetime, that seems to be asking what theory would be true if the currently best verified theories were wrong? There is no meaningful way to answer that. It is not like picking matter without electric charge, which is possible. There is just no theory left if you remove spacetime.
Yes, I've used this example many times (stars as dust; implements hypothetical smooth Oppenheimer-Snyder type collapse), as a way of talking about what you would see throughout a collapsing volume, and also to discuss how radical a change to classical GR is implied by 'active horizon' hypotheses (e.g. firewalls).
More like a black dwarf, with different composition than any that form naturally (none are iron). But, yes, I forgot the stage of electron degeneracy. The only stage that would release much energy is the neutron star formation, when an enormous surge of neutrinos are released.
No, whatever remains has nothing to do with a star.
No, the mass stays the same.it is behaving as though the mass has gone to
It doesn't. It behaves as if the mass is M, the mass while the star was 'normal'. Inside the horizon, you have a curvature singularity, but this does not represent mass.
That just says it has a history that has led to its internal energy, which is a crucial point that for some reason often gets overlooked when people use language that suggests this history, and the associated energy density, just vanish once the energy generation turns off. Of course that's not correct, the energy is still there, and so is the hydrostatic equilibrium. So the issue is always about tracking what happens to the heat-- nothing would ever happen if heat were not being lost, so the issue is, how fast is it being lost, and can force balance be maintained on that timescale. So it's always about the thermal timescale, not the absence of a possible force balance.
Not so, this is only if you assume the white dwarf is at zero temperature, which is the common assumption. That requires that the white dwarf has a substantial history of cooling, and that's exactly what it will not have if you are adding mass to it-- you have to track the timescales for cooling, compared to the timescale of the added mass. Sure, if you add mass slowly enough that the white dwarf always cools to zero temperature, then the Chandra mass is relevant-- but that's also the case that will not lead to any core collapse, just a gradual contraction in hydrostatic equilibrium right up to the formation of a neutron star. So what actually causes the collapse is the thermal instability that kicks in when you get close to the Chandra mass, and that doesn't care how slowly you add mass because it is an instability, not a bifurcation. The term "catastrophe" is a bit ambiguous about that distinction.
I don't know what you mean by that, it is perfectly standard for a protostar to be doing that, and be in hydrostatic equilibrium (it's just a quasi-steady equilibrium, but so are all equilibria, there is no such thing as any other type.)
What I'm saying is that there would never be any collapse if the temperature really stayed near zero. In other words, if we use the usual white dwarf idealization, which is a zero temperature, we are saying that the process is happening slowly enough for the heat to keep leaking out and maintaining zero temperature-- and you'd never get a core collapse in that case, so that cannot be the correct description, even though it is formally the meaning of a Chandrasekhar mass. This doesn't mean the Chandra mass is not relevant, or that Chandrasekhar was wrong, it just means that the Chandra mass is simply a benchmark-- the way it is derived cannot be taken as the physical process that actually produces core collapse, that would miss what is actually happening there.
That's why I also mentioned that you could have mass falling into the core that already has a high internal energy, as when you build an iron degenerate core that is built from the high temperature of shell fusion of silicon or some such thing. That it is at such a high temperature, and not zero temperature, is the reason it has access to thermal instabilities like photodisintegration and the Urca process. Again the key point is that the actual physics of core collapse must be a thermal instability, not a hydrodynamic instability, because the energy is there to create hydrostatic equilibrium-- the zero temperature assumption is not formally correct, it only works to get the benchmark mass where the thermal instability is going to rear up.
Yes, I agree that GR could throw a monkey wrench into the picture, such that it would not need to be a thermal instability, it could be a mechanical instability related to orbital instability. I'm not sure how important this is for the whole process of core collapse, as it seems like a rather late-stage event in the whole core collapse process (and may relate more to whether you get a neutron star or a black hole, more so than why you get a huge energy release from core collapse).
Yes, any physical explanation is going to have to idealize the solutions, and so the two limits often invoked are the quasi-static limit of force balance, and the opposite limit of free-fall. Core collapse is generally regarded as a decent example of the latter, but my point is, this is often incorrectly attributed to the absence of a possible force balance when the mass gets high, independent of the other necessary assumptions that get swept under the rug. I'm saying that given the kinetic energy content that is in there, there is a possible force balance-- so what causes the core collapse must be the thermal instability that rapidly removes that kinetic energy, either via neutrino escape or photodisintegration of iron. Those processes are good at removing kinetic energy but require that the temperature remains high, so they self-regulate the thermal environment in a way that doesn't care how quickly mass is being added once they take on a life of their own. The hydrostatic analysis that gives us the Chandra mass tells us the mass benchmark where this will happen, but it still wouldn't happen without the thermal instability that siphons off the gravitational energy and converts contraction into collapse.
Yes that's the point-- the supernova occurs because the thermal timescale can be that short. So the problem is not the absence of a possible force balance, it is the presence of a really short thermal timescale.
Again, it can support itself if it is not at zero temperature. And if it gradually approaches zero temperature, it will be in force balance all the while, and just become a black hole, with no core collapse ever, before the temperature ever reaches zero. That this is not precisely what happens is simply a matter of the very short thermal timescales owing to the processes that remove kinetic energy.
And the Chandrasekhar mass is a zero-temperature limit, so again the issue is always, how is that limit approached-- in short, what is the thermal timescale.
The point is, there are quasi-stable states available there, they simply involve a lot of kinetic energy that prevents complete degeneracy from appearing. If we turn off the thermal processes that remove kinetic energy, such as the Urca process and photodissociation (neither of which appear in the derivation of the Chandra mass), then we never get a core collapse. What Chandrasekhar showed with his celebrated mass limit is that a white dwarf of that mass must contract. That it contracts in a free fall core collapse is all about the thermal processes, processes that do not even appear in the derivation of the Chandra mass. In short, people miss a big part of the story of core collapse when they go straight to the Chandra mass and assert things like "no force balance is possible so you must have a free fall", that's what is wrong. What is right is that no force balance is possible at the end of a process of releasing or locking up heat, but whether or not that leads to a collapse requires analysis of the thermal processes and their timescales because core collapse is a thermal instability, not a hydrodynamic one.
The difference in those equations of state brings in a new issue, which is whether or not you get a core bounce and an explosion. That's separate from the issue of whether or not you get a free-fall core collapse. If neutrons had exactly the same equation of state as electrons, we'd still have core collapse in much the same way we have now, because the thermal instability has nothing to do with that equation of state. We just wouldn't have core bounce, and we wouldn't have neutron stars, we'd just have the rapid and relatively quiet collapse into black holes that we think we now get with very high mass stars.
No, the equation of state is not about what happens while you are turning electrons and protons into neutrons, it is about what you have after that is all over with (higher mass particles with strong forces and strong gravity). That's all relevant to the core bounce as the equation of state stiffens. The thermal instability simply involves the removal of heat as neutronization occurs, which is different from the forces that neutrons experience after they form. In other words, one shows up in the energy equation, and the other in the force equation. The neutron equation of state involves effects that reduce how relativistic the particles are because there are no more low-mass electrons, and there are repulsive forces between the neutrons (not degeneracy, that isn't a repulsive force it's just the kinetic energy content there), so that stiffens the pressure and generates the core bounce. But the core collapse is a thermal instability, it shows up in the energy equation when we see that lots of kinetic energy is being locked up or lost.
There is a lot of confusion about the adiabatic index in an equation of state. If the process were really adiabatic, the connection between pressure and density always looks like a 5/3 power law for nonrelativistic gas, and 4/3 for relativistic, regardless of degeneracy (though since neutrons experience other forces, you can get below 1 for them, if the process is adiabatic-- like a zero temperature condition). But the process is not adiabatic, and the temperature is not zero, there is important heat content because the gas is at some kind of fusion temperature initially. So we must track the thermal timescales, we must follow the heat. If we could really do that by simply asserting the zero-temperature equations of state for electrons and/or neutrons, we'd never get a core collapse, because if the temperature stays zero, the radius is always a continuous smooth function of the mass and the composition, both of which vary continuously as we add mass to create the contraction. That smooth solution assumes a quasi-steady force balance at every stage of the way, so is appropriate for a slow enough rate of adding mass (the "particle by particle" approach mentioned in the OP). But that is not what would really happen, because the temperature is not zero, there is heat locked up in the star that prevents contraction until thermal processes allow that heat to be removed. If there are thermal processes that remove that heat in an unstable way, you get the thermal instability that produces the core collapse. If there are not thermal processes that remove heat in an unstable way (i.e., that don't runaway until they happen faster than the sound crossing time), then you can keep all the same equations of state, and you'll still never get a core collapse if the rate you are adding mass is slow enough-- which is what I believe the OP was asking about.