[Airthumbs (OP)]

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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?

If an object has infinite density then it must have mass?  And for that density to be infinite so must mass/energy?

[pzkpfw]

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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?

If an object has infinite density then it must have mass?  And for that density to be infinite so must mass/energy?

Yes it has mass. But not infinite mass. Please re-read the posts by Eternal Student and Kryptid. This is covered.

[Eternal Student]

Hi.

and yet it seems there is a consensus towards infinity and zero which when you think about it is very counterintuitive.

   Stay calm and take a bit of time to read the replies if you want to.   When I first used this forum I had a lot of trouble keeping track of who was who.    You aren't always getting the "quote" system to work properly and sometimes it appears that a different contributor had said something from a different person - but that's ok,  the forum isn't easy to use and I know I got it wrong several times.   It can seem like a "them" vs. "me"  situation but it isn't.   "They" aren't collaborating, "they" are just people giving up some time and trying to help or join a discussion.   Indeed "they" will sometimes make mistakes and that includes me.   Sometimes there may be a few people with some other agenda, it's a public forum so anyone can use it.  You can usually spot people who are just trying to advertise something, for example.   If there's a big problem then there's a "report" button at the bottom of the post somewhere and you can have a moderator look at the post - you don't use that if the only problem was that you don't agree with them (it's meant for when the post has become threatening or breeched the policies etc).

   As far as I can see the following people have contributed to this thread so far:

You  ( @Airthumbs ).
@paul cotter
@Kryptid
@pzkpfw
@Halc
Me  ( @Eternal Student )

Of those only 2 have made any comments relating to size or density of the singularity.   One of those was me and I have tried to put the brakes on trying to measure the size or density of the singularity.   So that leaves only 1 who may have started to use this language and that isn't much of a consensus or majority.
 

Nearly all of the responses to my question have included information about a singularity being infinite and of zero size

     Only if you've also been discussing it on other forums or other places.
One of the phrases that has repeatedly come up in several replies is that  GR (General relativity) is only an approximation.  The appearance of a singularity at r=0 is certainly a concern and one of the main things that suggests GR is simply failing to describe this extreme situation and some new theory like a quantum theory for gravity may be required.

Best Wishes.

[paul cotter]

A value of, or approaching, infinite density can arise in two ways: (1) infinite mass in a finite volume or (2) finite mass in a zero volume. It was (2) that several posters were alluding to and the "infinite mass" in the singularity is an unfortunate misunderstanding by the OP.

[Airthumbs (OP)]

I am under the impression that it is not possible to state what is inside a black hole as we lack the tools currently to investigate. So it is a learning curve for me to discover that some people use theory as fact.  This is relating to the existence of a singularity or lack of and to take that concept further.  It has been highlighted during my responses that my idea seems speculative, and yet some people are telling me the physical aspects of a singularity as if it were fact and this is something I must consider when using this forum.

I value the expertise and insights from the responses and I very much appreciate the time people have taken in an attempt to try and answer my question.  I have learned a lot but also I feel I have learned that some scientists are blinded by theory and maybe have become a little blind or bias to reality.

I think the word "if" should be used more when relating to theoretical ideas rather than giving facts on theoretical ideas which are not proven or measured in anyway.

A black hole does have mass, we know that, we know how much mass it has due to the gravitational influence it has on other objects nearby.  We calculate the mass of a black hole using solar masses as a rubrik.  So we know the mass.  Density, all we know is that the mass calculated must exist within that region of space time beyond the event horizon, thats all we know. We don't know if there is a singularity, we don't know the density of said theoretical singularity.

And so that brings me back to my original question after side stepping the theoretical responses which to me seem far fetched to say the least.

Maybe a better approach would be for me to ask this......   a black hole has a given mass, we know the size of space it occupies.   I am sure it is possible to calculate the following.... given the mass we know for any given black hole and the physical size of the blackhole at what density would that mass need to be to fit inside the physical area?

I mean literally think of it as a sphere of matter condensed no further than it needs to be to fit inside that physical region of space we can observe where a black hole is present. If said matter cannot fit inside that region of space given our current understanding of physics then I will be more open to theory.

Best wishes and thanks again for taking time to respond, I find it fascinating.

[Kryptid]

 hmmm... mostly OK.
     We know any particle of mass m cannot hold a constant radial co-ordinate r  once  r<Rs,  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.

And so it appears that my understanding of an infinitely-dense singularity is an artifact of the "pop sci" explanation of black holes. I learn something new all the time. Now that I think about it, this is essentially a "divide by zero" problem. That would make the answer undefined as opposed to infinity.

Maybe a better approach would be for me to ask this......   a black hole has a given mass, we know the size of space it occupies.   I am sure it is possible to calculate the following.... given the mass we know for any given black hole and the physical size of the blackhole at what density would that mass need to be to fit inside the physical area?

That's more or less the Schwarzschild radius equation (or an alteration of it).

I mean literally think of it as a sphere of matter condensed no further than it needs to be to fit inside that physical region of space we can observe where a black hole is present.

But it isn't. The way that event horizons work is that all matter that crosses it must move inward. This is an effect of how distorted space-time is inside of the event horizon. The matter must move inward as inevitably as you or I must move towards the future. Space and time essentially swap roles like that.

I agree with you that no true singularity exists in a black hole. Relativity doesn't take quantum effects into consideration. We need a picture of quantum gravity to really know what happens in there.

[Origin]

I have learned a lot but also I feel I have learned that some scientists are blinded by theory and maybe have become a little blind or bias to reality.

That is probably because you don't really understand what they are saying.

I am sure it is possible to calculate the following.... given the mass we know for any given black hole and the physical size of the blackhole at what density would that mass need to be to fit inside the physical area?

The question as stated doesn't make much sense.  If I assume when you say the 'size' of a black hole you mean the event horizon, then it is a trivial division problem.  The mass of the sun is ~ 2 x 10^30 kg.  If that mass was a black hole the radius of the event horizon would be ~ 3 km or 3000M.  The volume would be ~ 1 x 10^11 m^3.  So the average density of the mass inside the event horizon is ~ 1.7 x 10^19 kg/m^3.  That number is of little use of course, since there is no known force or mechanism that can prevent the collapse of the mass to a singularity.
Is there 'really' a singularity at the center of a black hole?  The scientific answer is dunno.

[Halc]

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

Escape velocity and gravitational 'strength' are neither a function of density nor of compression, not even under Newtonian mechanics.
A black hole doesn't have an escape velocity. There isn't a direction a thing can go (at any speed) that is to the 'outside'. It would be like trying to throw a stone (or shine a light) into 2023.

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

There is no compression inside a black hole. Compression comes from a surface pushing back, like you get anywhere on a neutron star. Nobody has said there is no mass, but ES uses the term 'mass parameter'. Both mean the kind of mass that results in gravity and inertia. The 'mass parameter' is used to distinguish the term from meaning 'material'.

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

You've not identified any contradiction in the mathematics, so no, it doesn't seem off.

I keep thinking that mass and compression are the key here

There is no compression in a black hole. Sure, there is compression in a star in the process of becoming a black hole, but it isn't yet a black hole then. If you drop a large rock into a black hole with some sort of meter measuring the stresses on it, it will indicate tension, not compression, all the way down, including well before it crosses the event horizon. The rock will of course be pulled apart as it crosses the Roche limit, which may or may not be inside the event horizon. Phobos is currently approaching the Roche limit of Mars and is already beginning to break up.

And yet it seems the scientific consensus [...] is that once a black hole is formed it remains as a black hole regardless of it's mass?

If enough negative mass drops in, it eventually masses zero and becomes nothing instead of a 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.

No. Nobody says that.

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. 

There's no amount of mass that makes a black hole. There are no known means by which a small mass (like that of our sun) can be compressed sufficiently to collapse into a BH, but there are some hypotheses that small ones might have formed incredibly early in the birth of the universe, the so-called primordial black holes. These can be small.
The Schwarzschild solution is a vacuum solution. So for instance, take all the mass that currently exists in Earth's Hubble sphere (a ball about 15 GLY in radius).  The Schwarzschild of that much mass is a bit less than 15 GLY, and yet no black hole forms because that mass doesn't exist in what is otherwise a vacuum. So putting a bunch of matter into a sufficiently small space is not enough.

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.

There is no other radius that is different from its Schwarzschild radius. Perhaps you suggest a naked singularity, one whose say charge is sufficiently negative to prevent an electron from entering, despite the gravity of the situation.

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)".

By that comment I meant that there is no space occupied by matter inside a black hole. Yes, a 'radius' does definie a meaningful volume in Euclidean space, but as ES correctly points out, the spacetime in a black hole is not Euclidean and any 'density' computed in this manner is just a number, no corresponding to actual physical density of matter.

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).

This makes it sound like matter is still there, squashed into nearly a 'point' in space somewhere. This isn't so. The matter ends when time ends at the singularity, which isn't a point, but simply a region where standard physics is no longer capable of describing the situtation. The singularity is actually a line (Schwarzschild), cylinder plane (Kerr) or a fuzzy combination (Reissner-Nordstr?m) region where time simply ends, matter and all. So matter dropped in a different times ends up in different places at the end.

I do not agree that a singularity is of zero size.

Very good. It isn't size zero. But it also doesn't have a meaningful volume. An area maybe. One might express an average density of that area.

I am under the impression that it is not possible to state what is inside a black hole as we lack the tools currently to investigate.

This is false. By talking about black holes, you are already implicitly accepting the one theory (Einstein) that posits them, and given that theory, one very much has the ability to describe them.
Take an alternative theory like the Schmelzer theory which denies at least both postulates of special relativity. All the physical predictions are the same, but there is no big bang and no black holes. Matter falling in what are called 'frozen stars' just get stuck on the surface outsize where Einstein would put the event horizon. Time is paused there. Nothing gets compressed. The experience of falling into one of these is simply the end of time, similar to that of a black hole, but without all the nasty disassembly first by tidal forces. Infalling matter remains intact, under tension (never compressed), but in negligible volume, so arbitrarily high density as you measure it.

So it is a learning curve for me to discover that some people use theory as fact.

No theory is fact. If it was, it would be theorem, not a theory. That's the difference. One is proven, one is not.

Density, all we know is that the mass calculated must exist within that region of space time beyond the event horizon, thats all we know.

What we know from the outside is the no-hair theorem, where a black hole has but three properties and no more. Density is not one of the three things. There is nothing corresponding to the usual meaning of the term physical density.

Maybe a better approach would be for me to ask this......   a black hole has a given mass, we know the size of space it occupies.

No, we don't have a meaningful value for the 'size of space it occupies'. A black hole doesn't occupy space. All of its events are in the future of all events in the rest of the universe, so that makes it in a way something that doesn't yet exist at all, let along have a volume. You can jump into one and still see the universe outside, (can't do that with the Schmelzer theory), but the spatial volume is arguably infinite in there, or perhaps finite but super large, and it changes over time.
What there isn't is material. All the stuff that fell in a year ago? That doesn't exist anywhere, relative to say somebody jumping in. It's not squished into a small location somewhere. There's no squishing going on.


This is me doing the best I can explaining things. I am sure I have made mistakes, and would probably be significantly corrected on a forum with people who know this stuff better than I don.

[pzkpfw]

One thing I'd add for Airthumbs:
(A) Black holes were predicted based on current knowledge of gravity, atoms, etc: a bunch of stuff. Then evidence for their existence was found.
(B) It's not that they were seen first and a bunch theories were generated to explain them.

It'd be a pretty big coincidence to find something expected by predictions that turn out to be entirely wrong.

That isn't to say everything is known (e.g. exact nature of the (not?) singularity), but if you want to dispute what a black hole is, you can't just fling ideas out like it's case (B), you need to understand the knowledge in case (A) and find where that's wrong.

[Airthumbs (OP)]

HALC are you an expert on the contents of a black hole?  I mean you keep stating there is a singularity inside a black hole as if you know that for a fact?

And you are quite right, I do not have the academic expertise in physics which is why I am using this forum. You almost seem offended that I would wish to participate in a discussion about something I want to learn more about.

However I still don't understand why you state emphatically that there is singularity inside a black hole when we just don't know what is inside in reality. I have found all of your responses to unhelpful and in fact you seem to enjoy pointing out that I do lack knowledge as you have used this rhetoric in one of my previous posts. now I don't bother reading them as it appears you quote me on everything except the fact that what you state is essentially fiction regarding a singularity.

[paul cotter]

Halc is simply trying to explain the intricacies of black holes by taking quotes and explaining the relevant errors. Unless one has a good grounding in GR(which I certainly don't) many statements may seem counter intuitive and difficult to grasp. I have never found Halc to take pleasure in correcting errors and I have seen him go to great lengths when some posters fail to understand some critical point with way more patience than I could ever muster. 

[Airthumbs (OP)]

Halc is simply trying to explain the intricacies of black holes by taking quotes and explaining the relevant errors. Unless one has a good grounding in GR(which I certainly don't) many statements may seem counter intuitive and difficult to grasp. I have never found Halc to take pleasure in correcting errors and I have seen him go to great lengths when some posters fail to understand some critical point with way more patience than I could ever muster. 

Evidently that patience is understandably wearing thin.......   here are a few notes I would like to add in response to certain statements that I found to be intriguing and subsequently would like to highlight them here......

1,Einstein himself did not specifically define black holes in his equations; rather, the concept emerged as a consequence of his theory.

2, Einstein's theory of general relativity provided the mathematical framework that allowed for the possibility of singularities to exist, particularly in the context of black holes. However, Einstein himself was initially skeptical about the existence of singularities.

3, When Karl Schwarzschild found a solution to Einstein's field equations that described a black hole, it contained a mathematical singularity at the center. This singularity implied a point of infinite density, which was a concept Einstein found troubling and at odds with his intuition about the physical universe.

4, Einstein interpreted the singularity as a mathematical artifact, suggesting that it might be a sign that general relativity breaks down under extreme conditions rather than a true representation of physical reality. He famously referred to singularities as "naked" singularities, indicating a problem with the theory rather than a physical phenomenon.

OK, so it seems I and Einstein share something in common, however, I still reckon a black hole is just a very dense object and the singularity as I said before is a creation of math to justify the solution, and in a much more scientific way I believe that Einstein basically said the same thing.

[Eternal Student]

Hi.

HALC are you an expert on the contents of a black hole?

   He hasn't been inside one and returned - but he is regarded as an expert on GR (General relativity) by most regulars.

Let's be objective for a moment:
    What will happen in most forums is that the regulars will start to rally around another established member.   We're just human beings so that will also happen here.  Fortunately, Halc is big enough to take a little knock back from someone so we don't need to worry about him too much.  Meanwhile, it should be apparent that hostility isn't going to win a lot of favour and people will just go and watch "Jerry Springer" if they want to see some friction.
   

the singularity as I said before is a creation of math to justify the solution, and in a much more scientific way I believe that Einstein basically said the same thing.

    Hmmm....   How on earth could the mathematicians be made to look like the "bad guys" in that?

Wikipedia has  several (20 ?) definitions for "singularity".   https://en.wikipedia.org/wiki/Singularity
This is the one mathematicians use:

 In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity

Example:     The equation   y = 1/x      has a singularity at x=0.      Why?   The variable y is well defined on all real values of x except when x =0   because division by 0 is not defined.

The Schwarzschild metric   has the term   (1 - r_s/r)    in it.
That's undefined at r=0   because there would be a division by 0. 

  .... and that's really all there is to it.

There is a mathematical singularity in that formula.   You can't change that.   It's just a statement about the behaviour of a mathemtical term.

What can happen is that another person, often a physicist, comes along and hears something else:

You say:   There's a singularity at r=0.
They hear:   There's a point in space where density become infinite.

The mathematicians weren't suggesting "the singularity" was viewed as some physical object or even as some point in spacetime.  The equations are singular at r=0 and no mathematical trick like a transformation of co-ordinates can remove that singularity.   Mathematicians go out of their way to consider the spacetime manifold for the Schwarzschild to be something that specifically excludes the point r=0.   Whatever it is, and it may be nothing at all,  that thing cannot be included in the same spacetime that I would also be in.    It's only a few people, mainly physicists, who decided a spacetime manifold shouldn't just have a hole or puncture in it, they wanted to include r = 0 as some sort of point in spacetime.

Best Wishes.