What happens when a Neutron Star forms a Black Hole?

[Tanelorn]

TL;DR Summary

What happens when a Neutron Star forms a Black Hole

Supposing the total mass of a stationary, non rotating Neutron Star is just one Kg below the mass required to form a black hole. Based on the wiki reference below the Schwarzschild radius must be just beneath the surface of the Neutron Star sphere.

Now supposing an object with a mass of one Kg collides with the Neutron Star, presumably the neutron star now becomes dark or in other words a black hole.

https://en.wikipedia.org/wiki/Schwarzschild_radius
"supermassive black holes have comparatively low average densities. (Note that a black hole is a spherical region in space that surrounds the singularity at its center; it is not the singularity itself.) With that in mind, the average density of a supermassive black hole can be less than the density of water."

So my question is, is the newly formed black hole still a neutron star inside its Schwarzschild radius, which is now dark because light can no longer escape? Or does the Neutron star simultaneously collapse to a near singularity? The only reason I am even asking this is because the wiki article mentions that it is possible for a large enough body of water to also be a black hole.

I have looked online for months, but could not find much to answer this question with certainty.

 

[PeterDonis]

Supposing the total mass of a stationary, non rotating Neutron Star is just one Kg below the mass required to form a black hole

There is no single "mass required to form a black hole". A black hole can have any mass.

Based on the wiki reference below the Schwarzschild radius must be just beneath the surface of the Neutron Star sphere.

No, this is not correct. First, the concept of "average density" is meaningless for a black hole (and the Wikipedia article is not a reliable source in this respect). Second, no stable object, whether it is a neutron star or anything else, can have a radius smaller than 9/8 of the Schwarzschild radius that corresponds to its mass. (This result was proved decades ago and is known as Buchdahl's Theorem.) So there is no way for a neutron star, or any other stable object, to be "just short" by an infinitesimal amount of being a black hole. There is a finite gap between the smallest possible stable object and a black hole of the same mass.

 

[PeterDonis]

the wiki article mentions that it is possible for a large enough body of water to also be a black hole

No, that's not what the article is saying, even when we correct for the fact that it is applying the concept of "average density" to a black hole, for which such a concept is meaningless.

 

[Tanelorn]

Thanks Peter, so does this mean this wiki statement below regarding the S radius overtaking ist physical radius is incorrect? If so then my understanding of this has been wrong for a long time...

"Therefore, as the body accumulates matter at a given fixed density (in this example, 997 kg/m3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses (1.36 × 108) M☉, its physical radius would be overtaken by its Schwarzschild radius, and thus it would form a supermassive black hole."I also have read articles in which two neutron stars collide and the total mass was sufficient to form a black hole. Is this much different to my question above where a small amount of additional mass is just enough to cause a black hole to form? Or is this also incorrect in some way?Is it correct that any time the S radius becomes larger than the radius of the physical body within, that the body within collapses at the speed of light to a virtual singularity, and all its mass and energy is
completely converted into warped spacetime, or in other words gravitational energy?

 

[PeterDonis]

does this mean this wiki statement below regarding the S radius overtaking ist physical radius is incorrect?

Yes. A good example of why Wikipedia is not a reliable source.

First of all, matter in the real universe does not accumulate at a fixed density. Objects get denser as they accumulate more matter, because the matter on top presses down more on the matter underneath.

Second, even in a highly idealized and unrealistic situation where an object somehow continued to accumulate matter at a fixed density, if it somehow survived without collapsing until its radius was 9/8 of the Schwarzschild radius for its mass, it would collapse then, while there was still a finite gap between its radius and the Schwarzschild radius for its mass.

I also have read articles in which two neutron stars collide and the total mass was sufficient to form a black hole.

Specific references would help, but yes, in general this is a possible process. It just won't involve any state in which a stable object has a radius only infinitesimally greater than the Schwarzschild radius for its mass.

any time the S radius becomes larger than the radius of the physical body within

If an object's radius is smaller than the Schwarzschild radius for its mass, it has already been collapsing for at least as long as it took to get from no smaller than 9/8 of the Schwarzschild radius for its mass, to the radius it has now. So describing it as "the S radius becomes larger than the radius of the physical body within" is mistaken. The S radius is not what changes during the collapse process; the physical radius of the body does. The collapse process involves the physical radius of the body starting from something more than 9/8 of the Schwarzschild radius for its mass, and then getting smaller and smaller, until finally it reaches zero and the collapsing object forms a singularity. At the point at which the radius is just equal to the Schwarzschild radius for the object's mass, an event horizon appears in the vacuum region outside the object at that radius and stays there. (Technically, before then there is an event horizon inside the object, which forms at its center and moves outward until it hits the object's surface, which happens at the same instant that the object's radius is equal to the Schwarzschild radius for its mass.)

collapses at the speed of light

This is not correct; there is no meaningful "speed" that can be assigned to the collapse.

all its mass and energy is
completely converted into warped spacetime

No. The warped spacetime already existed around the body, even before it started collapsing. The vacuum that is left behind as the object collapses is also warped, but the externally measured mass of the body never changes during the collapse process; in other words, the "mass" to begin with wasn't really a property of the body itself, it was a property of the warped spacetime around the body. That property is unchanged when the body collapses.

The matter and energy that made up the body disappears when the body's radius reaches zero and the singularity forms. At least, that's what classical GR says. Most physicists believe that in fact this prediction is a sign that classical GR is incomplete and that we need a theory of quantum gravity to tell us what happens at that point. Unfortunately, we don't have a theory of quantum gravity.

 

[Tanelorn]

Thanks Peter, for taking the time to explain this. It seems that Wiki needs an update! Or is it possibly because different people in the field hold slightly different views?

Peter said, "At the point at which the radius is just equal to the Schwarzschild radius for the object's mass, an event horizon appears in the vacuum region outside the object at that radius and stays there. (Technically, before then there is an event horizon inside the object, which forms at its center and moves outward until it hits the object's surface, which happens at the same instant that the object's radius is equal to the Schwarzschild radius for its mass.)"

Is it correct to say that when the mass and density of an object is sufficiently high that an event horizon forms, then the matter within the event horizon collapses. Presumably the location of the highest density is at the center of the body, so in the case of a body which was just dense enough, the collapse begins at its center?

In my original question, I wanted to ask if, when an event horizon appears inside (or outside) of a neutron star due to it accumulating mass, that the neutron star does not remain inside the new event horizon as a no longer visible neutron star, but collapses to a virtual singularity at the same time that the event horizon is formed?When looking for information for this question, I found some interesting numbers for density of different materials:

https://chem.libretexts.org/Bookshe.../Physics_and_Astronomy/Density_of_Black_Holes

 

[PeterDonis]

Is it correct to say that when the mass and density of an object is sufficiently high that an event horizon forms, then the matter within the event horizon collapses.

No. By the time the object is small and dense enough that an event horizon forms, even if we are talking about the instant when an event horizon forms at the center of the object and starts expanding outward, the object is already collapsing. In other words, the event horizon forming is always an effect of gravitational collapse, never a cause of gravitational collapse.

I wanted to ask if, when an event horizon appears inside (or outside) of a neutron star due to it accumulating mass, that the neutron star does not remain inside the new event horizon as a no longer visible neutron star, but collapses to a virtual singularity at the same time that the event horizon is formed?

As above, if an event horizon appears anywhere associated with the neutron star, the neutron star is already collapsing. The neutron star will keep collapsing until it reaches zero radius and forms a singularity. To an observer falling inward along with the neutron star, the event horizon forms and emerges from the star's surface before the star reaches zero radius and forms a singularity.

 

[russ_watters]

Let me apply another angle to this:

Is it correct to say that when the mass and density of an object is sufficiently high that an event horizon forms, then the matter within the event horizon collapses.

You have the cause-effect relationship backwards: the collapse happens because the object is unable to structurally support itself, and the black hole formation is the effect. Not the other way around.

Presumably the location of the highest density is at the center of the body, so in the case of a body which was just dense enough, the collapse begins at its center?

That is correct.

 

[PeterDonis]

That is correct.

I don't think what he said is correct, because he said "a body which was just dense enough", which in the context of his other posts means "just dense enough to form a black hole". And as I have already pointed out, there is no such thing as a stable object which becomes "just dense enough to form a black hole"; there is a finite gap between any stable object and a configuration of matter which is "just dense enough" (any configuration of matter which meets the latter criterion must have already been collapsing for a finite time).

 

[russ_watters]

I don't think what he said is correct, because he said "a body which was just dense enough", which in the context of his other posts means "just dense enough to form a black hole".

Yeah, agreed -- in that context it is wrong for the reasons cited. If instead "just dense enough" is just dense enough to collapse, then yes the collapse starts from the center because that's where the density is highest.

 

[PeterDonis]

the collapse starts from the center because that's where the density is highest

I think this might actually depend on what triggers the collapse. For an object like a compact neutron star that is near the Buchdahl Theorem limit, yes, I would expect the inability of pressure to keep up with gravity at the center to trigger the collapse. That seems to be the kind of case imagined in this thread. But for other cases, such as a star going supernova, it might possibly be different.

 

[PAllen]

Another point is the nature of the horizon as a nondetectible sureface determined by the entire future of the universe. Specifically, if a neutron star will accrete matter in the future such that it collapses to a BH (.e.g. passing through a large dust could), the horizon begins to grow from the center out. But the same neutron star state not surrounded by a cloud will have no horizon.

 

[PAllen]

It is possible to discuss density of a BH before a singularity forms. Density can be defined as a local quantity by a comoving tetrad. It is then perfectly meaningful to discuss density distribution inside a BH, and average density, along any foliation slices that don’t include the singularity.

Further, the physically implausible momentary state of body of liquid water large enough to be inside its SC radius is a valid Cauchy surface that violates no energy conditions, and thus can be evolved back in time to earlier states that can produce it, that also violate no energy conditions. My intuition suggests that a huge shell of water vapor of just the right density distribution, undergoing self collapse, could have such a transitory state.

 

[PeterDonis]

It is then perfectly meaningful to discuss density distribution inside a BH, and average density, along any foliation slices that don’t include the singularity.

Technically, yes, this is possible. But you will have a much harder row to hoe if you try to defend the claim that this is what the Wikipedia article quoted earlier is doing when it talks about the density of a black hole.

 

[PeterDonis]

the physically implausible momentary state of body of liquid water large enough to be inside its SC radius

I'm not sure what you are trying to describe here, but if it is a state that is (a) momentarily "at rest" (i.e., on some spacelike surface, all of the small fluid elements of the body of water are at rest relative to each other) and (b) has a radius less than the Schwarzschild radius for the mass of the body of water, then no, no such state is possible. Any state of matter which has a radius smaller than the Schwarzschild radius for its mass must be either expanding or contracting.

 

[PAllen]

I'm not sure what you are trying to describe here, but if it is a state that is (a) momentarily "at rest" (i.e., on some spacelike surface, all of the small fluid elements of the body of water are at rest relative to each other) and (b) has a radius less than the Schwarzschild radius for the mass of the body of water, then no, no such state is possible. Any state of matter which has a radius smaller than the Schwarzschild radius for its mass must be either expanding or contracting.

I did not mean to imply at rest. I described it as a momentary density state of a collapse, thus not at rest. Simply that along some chosen Cauchy surface, the local state of each element is liquid water, but no constraint about their relative motion. That has to be adjusted (solved for) to make sure e.g. the dominant energy condition is nowhere violated. This latter requirement is what prevents momentary rest, because in the given geometry this would require a spacelike tangent vector.

 

[PAllen]

As I mentioned in another thread, a much more plausible example to explain how being inside an event horizon says nothing about density is a planet falling into a supermassive BH, where it would suffer no major effects for a while after crossing.

 

[PeterDonis]

I did not mean to imply at rest.

Ok. Yes, if the body of matter is collapsing, there can be possible states inside the Schwarzschild with pretty much any density you like, provided you make an appropriate choice of the total mass of the system (which, in order to allow states in the collapsing phase inside the Schwarzschild radius with densities like that of water, will have to be supermassive).