[Airthumbs (OP)]

I am not sure why we should consider black holes as something so odd when I think the answer has been with us for some time......

We know there are two things that define the type of star we get, mass and density in space time.  I think I got that right!  So we calculate the type of star from the amount of mass in a given area. Our sun for example, we know will not become a black hole as it does not have sufficient mass to collapse down that far.

As the mass increases and pressure then we get different types of stars that result in objects incredibly dense, such as a neutron star. This is at a point where the density becomes so high that it overcomes the electrostatic repulsion between protons, allowing them to merge with electrons to form neutrons. 

The pattern here seems to be that with increasing density, pressure and mass the atomic bonds of atoms themselves are altered under these conditions creating these dense objects.

Up until this point all the objects are known as stars.  Then we get to a black hole, now I see a black hole as just another type of star, a star where the density, mass and pressure have reached a point where it causes the particles in the atoms to become so squashed together that it allows for the creation of this super dense object aka a black hole. 

As we now understand blackholes are not eternal objects and I think the idea of infinite mass is just silly.  Nothing is infinite and cannot be, it is a mathematical concept that should not be applied to real world physics.

Black holes lose energy though Hawking radiation until it is thought they just kind of evaporate away. However I say that is not the case and cannot be the case.  What must happen is that after the density of the Black hole reaches a critical point, where the pressure is no longer able to maintain a singularity, then the black hole, or black star as i like to think of it as, becomes a different type of star, one that is visible again and maybe, just maybe these newly discovered Quark stars might be the candidate I am postulating should exist.

I bet there must be a pretty big bang when the black hole does snap into a less dense entity too?  I am not sure which way the energy would go, if you have an area where the very nuclear bonds between atoms is overcome what would happen when they are able to reform those bonds under less extreme conditions? 

[paul cotter]

A black hole has a gravitational potential so great that the escape velocity is greater than the speed of light. It is impossible for it to shine again like a regular star as light cannot escape. It takes a very long time for Hawking radiation to reduce a black hole and going on memory(dodgy!) I believe the necessary time scales would be far greater than the current age of the universe and no visible radiation can be expected from Hawking radiation until the very final stage where a flash of radiation would be observed.

[Halc]

We know there are two things that define the type of star we get, mass and density in space time.

That would result in a crude classification. Temperature would also be a significant factor, so I think the two-properties definition is incomplete.

As the mass increases and pressure then we get different types of stars that result in objects incredibly dense, such as a neutron star.

Black holes and neutron stars are products of supernovas. They don't just happen as mass increases. Exception: A white dwarf can become a type 1A supernova just by adding mass. These explosions are all pretty much identical and are used as standard luminosity candles across the universe, very useful for measuring distances accurately.

This is at a point where the density becomes so high that it overcomes the electrostatic repulsion between protons, allowing them to merge with electrons to form neutrons.

This assumes compression going on, and yes, supernovas are caused by compression, usually from a collapse of some kind, but not always.

The pattern here seems to be that with increasing density, pressure and mass the atomic bonds of atoms themselves are altered under these conditions creating these dense objects.

I see a black hole as just another type of star, a star where the density, mass and pressure have reached a point where it causes the particles in the atoms to become so squashed together that it allows for the creation of this super dense object aka a black hole. 

Not really. A black hole lacks the pressure. The geometery of one tends to pull things apart rather than squish them together. It is misleading to think of them as stars that are even more dense. They're not.

I think the idea of infinite mass is just silly.

If the universe is not of finite size, and has nonzero mass density, then it has to have infinite mass. That's not silly, it's unavoidable. It seems you might be in denial of an infinite universe, but there's nothing contradictory about it.

Black holes lose energy though Hawking radiation until it is thought they just kind of evaporate away. However I say that is not the case and cannot be the case.

Is this topic a speculation then?  I will move it to where speculations go since you're pushing personal beliefs.

What must happen is that after the density of the Black hole reaches a critical point

They don't have a density at all. For that, you'd need a meaningful volume. It does have a meaningful mass (that and charge and angular momentum. No more).

[SeanB]

When the density drops below the point that gravity escape velocity drops below C, the energy stored will likely start to radiate out from the zero dimension singularity. As it starts to exit, it becomes normal matter, at really high energy, and this essentially appears to the outside observer ( sufficiently far away for safety, probably around 20 light years away, behind a neutron star as radiation shield) as if there is a sudden burst of energy equal to the temperature of the original universe forming, and making all sorts of exotic matter as the energy converts to and from photons and matter. You probably will get kilotons of Oganesium being formed, simply from the inertia of the initial matter and the matter being ejected in the next Planck unit of time, and hitting the existing mass. This then will appear as a massive burst of radiation and very hard gamma rays, plus floods of neutrinos that suddenly can travel out of their prison, likely taking around 30% of the mass equivalent in energy with them. Going to be mighty unhealthy to be in the local vicinity, probably will sterilise all life within 1000 light years pretty effectively, and will be making all the heavy elements nearby, likely 20 light years, fission rapidly.  this is for something like a galactic centre mass object, smaller ones less damage, and if there are primordial black holes possible, you will find a lot of them created here, and be speeding out at close to the speed of light as well. imagine something the size of a proton in diameter, but with the mass of the sun, moving at 0.9C.

[Airthumbs (OP)]

It seems very counterintuitive for someone to state that the conditions applied to stars to calculate if enough matter is present for an eventually gravitational collapse does suddenly not apply to a black hole. 

Both Neutron Stars and Black holes are the result of matter being literally condensed, the matter must be there for the huge gravitational well to exist preventing light escaping in the case of a black hole. You cant just have an empty region of space, not only that but the mass of a black hole can be calculated so I don't understand the response of a moderator stating that there is no mass inside a black hole and that they only rip things to pieces.  That cannot be correct.

[pzkpfw]

... so I don't understand the response of a moderator stating that there is no mass inside a black hole ...

Where was that stated?

[Kryptid]

When the density drops below the point that gravity escape velocity drops below C

According to current knowledge, that's not how that works. The black hole just becomes a smaller black hole, and that one becomes a still smaller black hole. That continues until you reach a black hole of minimum possible mass (which is currently thought to be around the Planck mass, although some models put it much higher than that). Then you get that black hole vanishing in a final burst of Hawking radiation. Alternatively, it might also just sit there and not evaporate any further (if it's of the extremal variety).

[Airthumbs (OP)]

I want to clarify the following: 

The consensus currently is that a black hole can exist with a mass of one gram?

This seems a little off?  I keep thinking that mass and compression are the key here as that is what is required to bend space time and create this huge gravity well where even light cannot escape. And yet it seems the scientific consensus, amongst whom I don't know, is that once a black hole is formed it remains as a black hole regardless of it's mass?

The geometry referred to by a previous reply is simply the shape of the gravity well as a direct result of the presence of condensed matter, I don't see how that remains unaltered when there is a change in mass, specifically relating to the ability of that mass to bend space time into the geometry required to form a black hole.  If there is not enough mass to form that geometry then how can it maintain that shape?  I also expect that the critical mass to form a black hole is known and anything below that mass and condensation will not be able to form the geometry of a black hole.   

Finally if black holes persist for such a long period of time and only end their lives in a wimpy pop of hawking radiation then we should be observing black holes of all sizes everywhere as they would be the most common cosmological entity.  These black holes according to the consensus could be anything from the size of a grain of salt to a water melon and do not require mass to exist?

I also think I am right in stating that Planks law must be modified for it to be applicable to black holes as they are not themselves black bodies that emit radiation from a thermal source. The Hawking radiation from black holes represents a loss of energy, leading to a decrease in the black hole's mass over time.

From what I understand to be the consensus I see that it attempts to deal with the end of a blackhole through quantum mechanics in that eventually when the black hole reaches a mass of plank, probability and uncertainly become the ultimate fate of our black hole. I feel that someone has jumped the gun a little on the life cycle of black holes and missed out a key factor which is mass and compression. Without it, there is no hole?

[Kryptid]

The consensus currently is that a black hole can exist with a mass of one gram?

Yes.

If there is not enough mass to form that geometry then how can it maintain that shape?

Take a look at the formula for the Schwarzchild radius: https://en.wikipedia.org/wiki/Schwarzschild_radius

For any finite mass, a radius exists where an event horizon will form if that mass is concentrated inside of it. It's density that forms a black hole, not mass. However, that formula is a classical one, not taking into consideration the possible quantum effects that may put a lower limit on black hole mass.

do not require mass to exist?

No one said that a black hole of zero mass can exist.

Finally if black holes persist for such a long period of time and only end their lives in a wimpy pop of hawking radiation then we should be observing black holes of all sizes everywhere as they would be the most common cosmological entity.

It's quite possible that they are very common. However, they are also black. That means that only way we can observe them is through their gravitational effects (or if we get lucky enough that a stray, super-high energy particle from an evaporating black hole hits our detectors).

[Airthumbs (OP)]

I read up on the Schwarzschild radius concept.  From what I can infer from the information it seems that this is used to define a black hole using the amount of mass it takes to create one. 

"Black holes can be classified based on their Schwarzschild radius, or equivalently, by their density, where density is defined as mass of a black hole divided by the volume of its Schwarzschild sphere, Schwarzschild radius is linearly related to mass" (WIKI).

So from what I can tell from reading about this is that it actually seems to support the possibility that once the black hole does not contain enough mass to maintain the gravity well it's radius would become larger than its Schwarzschild radius and is no longer a black hole as light can then escape.

[Airthumbs (OP)]

In response to this; What must happen is that after the density of the Black hole reaches a critical point....

HALC "They don't have a density at all. For that, you'd need a meaningful volume. It does have a meaningful mass (that and charge and angular momentum. No more)".

I found that in fact density is a vital part of calculation for the Schwarzschild radius of a black hole.  And in fact that to exist smaller black holes must have an increased density. The increased density ultimately sets the size limit of  black holes with smaller sizes based on the particles being squashed more, until we reach the limit of what can be squashed.

 "A small mass has an extremely small Schwarzschild radius. A black hole of mass similar to that of Mount Everest would have a Schwarzschild radius much smaller than a nanometer. Its average density at that size would be so high that no known mechanism could form such extremely compact objects." (WIKI)

So as a black hole gets smaller it must increase in density to maintain the Schwarzchild radius.  And in fact you cannot get a back hole with a smaller mass than Mt Everest according to Wiki anyway.

How can an object that is loosing mass become more dense as that is the requirement for a black hole to persist as it gets smaller in size and to maintain it's Schwarzschild radius?

[Airthumbs (OP)]

When the density drops below the point that gravity escape velocity drops below C

According to current knowledge, that's not how that works. The black hole just becomes a smaller black hole, and that one becomes a still smaller black hole. That continues until you reach a black hole of minimum possible mass (which is currently thought to be around the Planck mass, although some models put it much higher than that).

I am a little confused by the improbable existence of such small back holes and in fact for a black hole to reach Plank mass it's impossible?  The material required to maintain a Schwarzschild radius does not exist at the density required within such a small volume.

[Eternal Student]

Hi.

I want to clarify the following:

The consensus currently is that a black hole can exist with a mass of one gram?

Yes, pretty much true.    Hawking radiation from it may now be quite energetic and frequently emitted so that the Black Hole would be fairly short lived.

the scientific consensus, amongst whom I don't know, is that once a black hole is formed it remains as a black hole regardless of it's mass?

   Yes.   It can also grow if it absorbs more mass (or something with a mass parameter like another black hole).

The geometry referred to by a previous reply is simply the shape of the gravity well as a direct result of the presence of condensed matter,

    Sounds very much as if you're basing everything on models of Newtonian gravity.   Assuming Newtonian gravity then, yes, some dense matter should be at the centre of black hole.   If you don't assume Newtonian gravity but use GR instead then you don't need vocabulary like "gravity well", gravity isn't a force and the source of gravity is anything that provides a component to the stress-energy tensor.   So that mass is one source but pressure or a flux of momentum across a surface is also a suitable source.
     Finally we need to mention that simple Black Hole solutions such as the Schwarzschild solution for the Einstein Field Equations are actually vaccum solutions.  This is possibly a little complicated to explain but the important point is that they describe a solution in a region of spacetime where there is no source of stress-energy.   The Schwarzschild solution is static - the metric and curvature of spacetime does not change or depend on time.   GR doesn't need to care too much what may or may not have been the original cause of that curvature,  once such a curvature exists in a vcacum it will be static (unchanging with time).

I don't see how that remains unaltered when there is a change in mass

     It doesn't.   Black Holes have a mass parameter and if something with mass falls into a black hole then its mass parameter will change (see later for one example).   Also if some mass enters a region around a black hole then the Schwarzschild solution is no longer an exact solution for the region - as mentioned it's a vaccum solution so there cannot be any mass in the region.

If there is not enough mass to form that geometry then how can it maintain that shape?

    I'm not sure exactly what is being stated here.   If you change the mass parameter of a black hole then there is some change in the curvature of spacetime.   For example, a one solar masss BH has the space around it return to nearly flat Euclidean space over a short distance along the radial co-ordinate r.   A 100 solar mass BH  would still show significant curvature of space at this distance.    The "shape" is much the same but there is certainly some scaling.   Consider a graph of  y = 1/x   versus  y = 100/x.


graphs.jpg (225.62 kB . 1403x896 - viewed 265 times)

These have the same "shape" y=1/x  but the blue one is scaled (stretched) up the y-axis.   So the red graph looks flat enough at about x-axis position 12 units, while the blue one is still coming in with a significant gradient there.

If there is not enough mass to form that geometry then how can it maintain that shape?

     See above:
(i)  Changing the mass parameter of a BH maintains only the shape or geometry of spacetime but there is certainly some scaling.
(ii)  The Schwarzschild solution is a static solution of the EFE, it does not change or evolve with time.   That is interesting if you assume that "time" is some god-given thing that exists, it always is just one thing we could define and identify without reference to anything else like a metric or some frames of reference.  If you don't assume that then the result is less of a surprise.   
     When we go about solving the EFE (Einstein Field Equations) we do so without knowing exactly what our co-ordinates are going to mean or represent.  For the Schwarzschild solution we may naively assume they are something like spherical (r, θ, φ) co-ordinates for space (so r = a radial co-ordinate from the centre of the Black Hole and θ and φ are polar and azimuthal angles)  with t as a time co-ordinate.   However, we don't know exactly what the co-ordinates were representing until the full solution of the EFE is actually in our hands.   It turns out that the r co-ordinate is not a space-like co-ordinate everywhere.   When r < R_s  this co-ordinate is actually a time-like co-ordinate and  t becomes a space-like co-ordinate.   It is apparent that r and t are not the space and time co-ordinates we naively thought we might have when we began to obtain a solution to the EFE.       
    I know that's complicated so let's phrase it a different way:   You may be willing to accept that near a massive object time flows at a different rate to a place far away from the massive object.  You may also accept that time flows at different rates according to movement through space.   Time is not universal.    Once we have a black hole in close proximity, time has been morphed in various ways.  It just so happens that with respect to that time which we have around a black hole,  the curvature of space shows no change with time.   It is impossible to say that the Schwarzschild solution was unchanging with respect to some universal time or if it is just that time has been morphed so much around the black hole that any object in the vicinity of the black hole cannot observe any change in the curvature of space around the black hole.
     Anyway, you seem to be worried about whether the gravity around a black hole object should change with time.  It doesn't have to,  the Schwarzschild solution is a static (time unchanging) solution for the EFE in a vaccum.  It's not necessarily coincidence,  the black hole has "cheated" and morphed time to ensure this will happen.

Finally if black holes persist for such a long period of time and only end their lives in a wimpy pop of hawking radiation then we should be observing black holes of all sizes everywhere as they would be the most common cosmological entity.

    I don't know why you think they would have to be the most common - but they do seem to be fairly common.

(i)  Finding the big Black Holes:   When the LIGO gravitational wave detector was switched on, we thought we'd have to wait years to find anything but we didn't.   Within a few minutes (not sure of exactly how long but basically short), we found something.   Since then we've been finding plenty of clear examples of BH mergers every year.   

(ii) Finding the small ones:  This is actually much harder.   At a distance r > the tiny Schwarzschild radius,  a small black hole of mass parameter δm exerts no more force on something than some ordinary particle of the same mass δm.    However, small black holes are one candidate for dark matter.  We currently think dark matter makes up about 80% of the mass in the universe.  So maybe primordial Black holes are extremely prevalent.

[Various other replies have also come in while I've been writing this and doing stuff - sorry, there may be some overlap and existing answers or discussion already given  etc. ]

Best Wishes.

[Eternal Student]

(I also started writing this yesterday in response to one of the very early posts you made.  I never got around to finishing it and posting it - but you ( @Airthumbs ) might as well have it ).

Hi.

Firstly, you should note that I'm not staff for the forum or anything special but I can spare an hour from my laundry duties and read your article.
Let's go through litle bits from the start.
     

We know there are two things that define the type of star we get, mass and density in space time.  I think I got that right!

     For main sequence stars, their mass and/or luminosity pretty much tells you everything.
     All you really have to tell us is just one thing - the mass of the star.  We can then find a model to predict the pressures and density at various depths into it and how this will change with time.

such as a neutron star. This is at a point where the density becomes so high that it overcomes the electrostatic repulsion between protons, allowing them to merge with electrons to form neutrons.

    Protons can combine with electrons (especially if anti-neutrinos are also available) to form neutrons.   There is no need for protons to get close to other protons for this process.    The main explanation given (for Neutron stars) is simply that there are too many electrons for such a small region of space and the Fermi exclusion principle will not allow two electrons to have the same quantum state.   There are protons available and it seems that the electrons will start combining with them to diminish the number of electrons occupying that space.

now I see a black hole as just another type of star, a star where the density, mass and pressure have reached a point where it causes the particles in the atoms to become so squashed together that it allows for the creation of this super dense object aka a black hole.

   OK,  that's speculation but not unreasonable and it could be like this.   If you assume that at least some of general relativity is right or a reasonable approximation for the spacetime around this dense object then some weird things are also going on.    You don't have to assume the GR model of a black hole is exactly right but at least be aware that time and space could be behaving quite strangely here.    As a result speculation about how these dense objects evolve with time, or move around in space can be quite wrong.
    We may all like to imagine a black hole as some simple object that behaves like a ball of stuff I can find in my back yard but nature just may not play by these rules.   It can have space and time behaving very oddly in this region.

and I think the idea of infinite mass is just silly.

    Not sure infinite mass was ever implied by anything.   Infinite density maybe.

However I say that is not the case and cannot be the case.

    That is an honest declaration of what is your opinion and you cannot be faulted for that.  Thank you.   Let's hear then what you think and why.....

What must happen is that after the density of the Black hole reaches a critical point, where the pressure is no longer able to maintain a singularity

     You don't explain how or why pressure would maintain a singularity and it's not obvious why it would.   Pressure does not cause or prevent a collapse of some material to a given region.  Pressure acts in all directions equally.   A pressure gradient is what you will need to cause a net flow of material from one place to another.   In the typical star, the pressure is greatest at the centre and falls off towards the outer surface, this causes an outward force that opposes further collapse of any material in toward the centre.   So a high pressure at or around the singularity may actually tend to push matter away from the centre rather than pulling matter there and maintaining a region of high density.

then the black hole, or black star as i like to think of it as, becomes a different type of star, one that is visible again

     No evidence presented or explanation for the how and why but OK... let's go on and see what you're thinking....

just maybe these newly discovered Quark stars might be the candidate I am postulating should exist.

     ...and this at least starts to imply the existance of something we might be able to find.   Can we find a star that is noticeably different to others and could have been an object that was a black hole and then evolved and switched on again as a star?   If we find one that will be great and some evidence in support of the ideas.
         There is already a theorised object called a "quark star" that you may have already seen or heard about (I don't suppose you would have used that term otherwise).   
(i)  It's theorised and not really supported with a lot of evidence yet.
(ii)  The evolution of a quark star is currently suggested to be from  Neutron star   to  a Quark star  and not something that happens via an intermediate stage that was a black hole.

if you have an area where the very nuclear bonds between atoms is overcome what would happen when they are able to reform those bonds under less extreme conditions?

    A theorised quark star shouldn't have recognisable atoms,  just some soup of quarks.   As such there may not be any inter-atomic bonds.

Overall Summary:
     The idea that some kind of matter remains inside "a region" we describe as the event horizon of black hole is not at all a silly idea and a lot of Astrophysicists may also harbour this view.   We can't get information out from anyone who has been in that region.   It may not be an ordinary region of just space which is why I put quotations around  "a region" (it's a region of spacetime and we won't worry too much about if it's just space).   Many physicists will assume that GR is just an approximation and it is going to break down somewhere.  Using it to predict what happens in a region of spacetime around  co-ordinate r=0 in a Black Hole is subject to some error.
     The remainder of your article is speculative but not offensive and not necessarily wrong.   It's very nice that you have an interest in the world around you and in Physics.
      Where you go from here is, of course, entirely up to you.   It may be worth keeping in mind that there is no shortage of "new ideas" or things that may revolutionise physics.   What is lacking are some extensions of existing theory, some demonstration of flaws in existing theory that may also lead to new discovery  and some new theory that is also well supported with experimental data or testing.

Best Wishes.

[Kryptid]

So from what I can tell from reading about this is that it actually seems to support the possibility that once the black hole does not contain enough mass to maintain the gravity well it's radius would become larger than its Schwarzschild radius and is no longer a black hole as light can then escape.

No, the event horizon radius would shrink in proportion to the shrinking in mass. Remember, all of the mass is concentrated into a singularity of zero size (this is why Halc says it doesn't have a meaningful density. Objects of zero size would have infinite density).

I found that in fact density is a vital part of calculation for the Schwarzschild radius of a black hole.  And in fact that to exist smaller black holes must have an increased density. The increased density ultimately sets the size limit of  black holes with smaller sizes based on the particles being squashed more, until we reach the limit of what can be squashed.

Density is important for when an object becomes a black hole. You can calculate the density of an object if all of its mass exists within its own Schwarzschild radius. However, it doesn't stay at that density. Since no force exists which can support a mass against such crushing force, it all collapses down into a singularity: an object of infinite density.

So as a black hole gets smaller it must increase in density to maintain the Schwarzchild radius.

We need to differentiate the density of a black hole as its mass divided by the volume of the event horizon versus the density of the singularity. All black hole singularities have the same density: infinite. What the wiki article is referring to is creating such a black hole from non-black hole matter (such as collapsing stars). It isn't referring to an existing black hole undergoing Hawking decay to become a smaller black hole.

The gravitational strength at the singularity is infinite is because the distances involved are zero. This is true for any finite value of mass. So even very tiny masses experience infinite gravitational force and thus the singularity cannot decrease its density to become something else.

However, all of these things are based on classical physics. It's quite possible that a black hole doesn't collapse to zero size due to quantum effects getting in the way. However, such a quasi-singularity would still be extremely small and extremely dense compared to anything else in the Universe.

[Eternal Student]

Hi again,

Let's do some of your ( @Airthumbs ) later posts but a bit more quickly.

I read up on the Schwarzschild radius concept.  From what I can infer from the information it seems that this is used to define a black hole using the amount of mass it takes to create one.

No or not well phrased.

   R_s   =  2GM/c².

Given any mass, there is always a corresponding Schwarzschild radius.

If, at some time, you were in a situation where this mass, M, was concentrated in a spherical region of space with radius < R_s   then a Black Hole would form.    However, the formation of a black hole may also be inevitably if you had lower density of matter.    We require only that the self-gravity of the particle is sufficient to compress it to a radius equal to the Schwarzschild radius.

You took this bit from Wiki:

where density is defined as mass of a black hole divided by the volume of its Schwarzschild sphere

  and just need to be aware that this is a definition of convenience.    The Schwarzschild radius is a number with units of length,  so we can imagine a sphere in Euclidean geometry of that radius.   The Black hole has a mass parameter which is a number with units of  mass.   We can divide the two things and end up with another number which we can call density and has units of   mass per cubic metre.

   However, we need to notice these things:
    (i) The mass parameter of the black hole doesn't force the existance of some matter with that mass at the centre of the black hole.
    (ii)  The region described by  r<R_s  in a spacetime diagram was not a description of a spherical region of space.   Assuming GR and the Schwarzschild solution correctly describes spacetime, that r co-ordinate has now become a time-like co-ordinate.

   So this density parameter is just a number with units that match a physical density.   There need not be any matter with a physical mass M in this region and "this region" certainly isn't a spherical region of space with radius = R_s.    The density parameter may not be describing the physical density of anything.

    In a later post you took a quote from @Halc that said much the same things:

HALC "They don't have a density at all. For that, you'd need a meaningful volume. It does have a meaningful mass (that and charge and angular momentum. No more)".

    The only minor difference I would prefer is that Black Holes have a "mass parameter" rather than something that is definitely a mass.   However, the mass parameter grows by  m   if the the Black hole absorbs a particle of mass m,   so there is some one-to-one correspondance between the mass parameter of a black hole and the mass that may have gone in to make it.

Anyway, your Wiki density quantity for a BH is not necessarily describing the physical density of anything.   With that understanding some of your later comments almost evaporate:

So as a black hole gets smaller it must increase in density to maintain the Schwarzchild radius.

    There is no need to assume we were ever talking about the physical density of anything.

And in fact you cannot get a back hole with a smaller mass than Mt Everest according to Wiki anyway.

    I've not seen that article but I'll assume it was talking about how you might form a Black Hole starting from a situation where you just have some mass and space is reasonably Euclidean to begin with.    You can try to squash the matter together.   Your target density is 
(3 c⁶) / (32. π. G³ . M²)       or    proportional to   M^-2   if I've done my calculations correctly.
    So when you have more mass  (bigger M),  you don't have to squash it together as much to form a black hole.
I'll assume Wikipedia then assumes some physical limit on how much we can squash particles of matter together.

    That is interesting but just puts limits on our ability to make a Black Hole when we're out here in flat Euclidean space with only some ordinary matter and bit of equipment to play with.
    I don't suppose a Black Hole out in space with a mass parameter that is only half the mass of Mount Everest cares if we could have made it by squashing some stuff together or not.   As previously mentioned, the density parameter for this black hole is just a number that may not represent the physical density of any sort of object or material it is required to mainatin at its centre.

Best Wishes.

[and again.... I'm still too slow and more replies have appeared....]

Remember, all of the mass is concentrated into a singularity of zero size (this is why Halc says it doesn't have a meaningful density. Objects of zero size would have infinite density).

     hmmm... mostly OK.
     We know any particle of mass m cannot hold a constant radial co-ordinate r  once  r<R_s,  it must travel to the singularity at r=0 where its worldine terminates.    However r=0 is a non-removal singularity in the Schwarzschild solution.  The Schwarzschild metric does not apply at r=0 and I really have no way to determine the size of the event or point at r=0,  if indeed that is an event that exists in my universe.  Only if you say "stuff it, I'll just put the numbers in anyway" will you be able to argue that the mass all ends up in a region of space with 0 volume.

Halc said this:

They don't have a density at all. For that, you'd need a meaningful volume.

     I would imagine Halc is implying the radial co-ordinate  r   at the Schwarzschild radius,   just isn't a spatial co-ordinate - but you'd have to ask him.

Density is important for when an object becomes a black hole.

   Looks like general agreement with what has been said by myself above.

We need to differentiate the density of a black hole as its mass divided by the volume of the event horizon versus the density of the singularity.

     Really worried about trying to find the density of the singularity.
     It's sufficient to note that the density parameter Wiki suggested isn't describing a physical density of some material inside the event horizon.

What the wiki article is referring to is creating such a black hole from non-black hole matter (such as collapsing stars).

   ...and we're back on the same tracks and in general agreement.

Best Wishes.

[Airthumbs (OP)]

Hi.

Hi there, thank you so much for your very detailed explanation. I am going to try and digest as much of it as possible over the next few days.  I think the reason I may have come across as Newtonian is because that is the physics used according to wiki to calculate the Schwarzschild radius.

Best regards....

[Airthumbs (OP)]

Remember, all of the mass is concentrated into a singularity of zero size (this is why Halc says it doesn't have a meaningful density. Objects of zero size would have infinite density).

I do not agree that a singularity is of zero size.  I have no reason for my disagreement other than it just doesnt seem to correlate with everything we can observe in the Universe.  I thought it was not possible to describe the singularity and yet it seems there is a consensus towards infinity and zero which when you think about it is very counterintuitive.

I am surprised actually that given what we know about space time and how mass effects it, that anyone could consider a singularity to have zero size and infinite mass.

Why do we need to have an infinite mass appear when we know what mass was required to create the black hole?  I think that a lot of these scientists must still be on that LSD test or something?

Oh and btw isn't infinite mass the same as stating infinite energy? You guys really think that a singularity has zero size and infinite mass?  Really? Seriously? Your not winding me up or anything?

[pzkpfw]

...
Oh and btw isn't infinite mass the same as stating infinite energy? You guys really think that a singularity has zero size and infinite mass?  Really? Seriously? Your not winding me up or anything?

What infinite mass?

[Airthumbs (OP)]

I have to add another little bit of research here and it must include the following paper:

"Do Black Holes have Singularities?
R. P. Kerr
There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose and Stephen Hawking then asserted that these must end in actual singularities. When they could not prove this they decreed it to be self evident. It is shown that there are counterexamples through every point in the Kerr metric. These are asymptotic to at least one event horizon and do not end in singularities".  https://arxiv.org/abs/2312.00841

The reason I added this reference to a recent paper by R. P. Kerr is that is seems anyone can pick and choose a side as we don't really know?  I am drawn to this paper as it seems to be a better approach to finding a solution than reverting to infinity in what seems a desperate attempt to continue with the current consensus which I and other top scientists disagree with.

Nearly all of the responses to my question have included information about a singularity being infinite and of zero size and yet one of the worlds leading scientists on this subject seems to feel that a singularity is a concept not found in real physics. And I would like to add that neither is infinity.  Infinity is a concept used to bodge the math to make it fit into a theory.