# Debate: Do black holes exist?

Discussion in 'Astronomy, Exobiology, & Cosmology' started by RJBeery, Aug 10, 2010.

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1. ### RJBeeryNatural PhilosopherValued Senior Member

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Surjective coordinate systems suffice for describing reality; no one doubts the existence of spheres. I am suggesting that injective coordinate systems do not.
You are over complicating things, but you have helped me reduce the thread to a single question, and for this I thank you:

True or false: back-reaction, as it applies to expanding the event horizon of a black hole, does not occur before mass crosses the existing event horizon.

Last edited: Aug 20, 2010
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3. ### prometheusviva voce!Registered Senior Member

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Your question is textbook example of the misuse of scientific words, however if you can restate the question "what happens to the horizon as matter falls into the BH?" I suggest you read http://arxiv.org/abs/gr-qc/0502040 and in particular the sections on thick shells and fluid spheres. Whether you'll understand it or not, I don't know.

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5. ### RJBeeryNatural PhilosopherValued Senior Member

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Thanks for the reference. Unfortunately, your alternative wording does not suffice due to the highlighted word. "When" this happens is exactly my point.

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7. ### prometheusviva voce!Registered Senior Member

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The paper answers that question.

8. ### RJBeeryNatural PhilosopherValued Senior Member

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I fail to see how this elucidates the issue.

9. ### prometheusviva voce!Registered Senior Member

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Epic failure. It's all there

10. ### RJBeeryNatural PhilosopherValued Senior Member

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As I quoted, the authors indicate that they analyze the BH with "zero energy fluid systems" because it makes the algebra simpler but does not change anything qualitatively from the outside reference frame. This means that, regardless of what this novel approach does in analyzing the mathematical BH model, the "when" has not been altered. Matter still apparently crosses the EH at t = infinity from the outside frame, and you making inane comments like "Epic failure. It's all there", implying that you've digested the paper and come to a different conclusion, doesn't change anything.

11. ### prometheusviva voce!Registered Senior Member

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I'm going to explain this one more time only, and then I'll leave you to your own ignorance because frankly I have better things to do than wipe away your figurative dribble.

Whether the black hole forms or not doesn't depend on what an observer at infinity perceives, it depends on what an observer that sits on the collapsing shell or sphere perceives. It is quite simple to show that a collapsing shell of sufficient energy will form a black hole at some finite time, undergraduates in physics that take the elective general relativity modules could show you the details.

Furthermore, if an observer far away from the black hole observes this type of collapse and concludes the black hole does not exist, because as far as he's concerned the matter sits at the horizon for ever, then decides to drop into the black hole as well he will get a nasty surprise when he gets to the horizon and finds himself inside the BH.

If you still think black holes don't exist, I suggest what you do is book yourself a ticket to the nearest one and throw yourself in. That way at least your nescient babblings will be obscured from us.

12. ### RJBeeryNatural PhilosopherValued Senior Member

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You are clearly on a different level than me, so thanks for your perspective Prometheus and thanks for participating.

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14. ### RJBeeryNatural PhilosopherValued Senior Member

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No, it was sincere. There is no doubt that you are on a different level from me. "Thanking" you for participating was a polite way of saying goodbye.

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15. ### AlphaNumericFully ionizedRegistered Senior Member

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Not so. Seeing as I've had complaints made about not providing detail lets do it the precise way first.

An n dimensional manifold M is a topological space, meaning it can be 'covered' in a set of open sets $\mathcal{U} = \bigcup \mathcal{U}_{i}$ which form a topology. For each open set $\mathcal{U}_{i}$ there is a map $\phi_{i} : \mathcal{U}_{i} \to \mathcal{V}_{i} \subset \mathbb{R}^{n}$ which defines a chart. Given the sets define a topology $\mathcal{U}_{i} \cap \mathcal{U}_{j}$ is a valid open set and in this case both $\phi_{i}$ and $\phi_{j}$ are valid charts. Therefore the map $\phi_{j}\circ \phi_{i}^{-1} : \mathcal{V}_{i} \to \mathcal{V}_{j}$ must exist and also be bijective, $\phi_{i}\circ \phi_{j}^{-1} : \mathcal{V}_{j} \to \mathcal{V}_{i}$ must also exist.

Putting that into more layperson terms coordinates are a description of a space we use, they are not something underlyingly physical. The bijective requirement means that if you are unable to convert one coordinate chart into another such that each point in the space is represented by one and only one set of coordinate values in each chart then you've extended your coordinates beyond their range of applicability. If you attempt to ignore this you find you are led to nonsense results as things like smoothness and differentiability are lost, your equations fail to reflect the thing you're describing.

This can be reformulated into a more preferable point of view by working in coordinate free formalisms or instead constructing things like topological invariants. A 2-sphere is topologically inequivalent to a plane, therefore you cannot cover a 2-sphere consistently using only one chart. If you add a 'point at infinity' to the plane then you can (its known as the Riemann sphere). If you don't then you need to cover the sphere in at least 2 'grids'.

This isn't something people just said "Oh I can't think of good coordinates" or "I don't like that I can't invert this", the fact there are structures which are inequivalent to Euclidean space is a huge thing. The notion that spaces can have geometry unlike Euclidean space was shocking even Gauss didn't publishing his work on hyperbolic geometry till after he was dead!

I've already linked you to an example of how a lack of global coordinates comes up in physics. There's an extension of that in QCD which relates to CP violation. The fact certain particle decay processes don't behave exactly symmetrically can be viewed as the fact you can't formulate global coordinates for a gauge field. That CP violation is the reason there's more matter than antimatter, its the reason we exist!

No, you are being naive. You don't understand the role multiple charts play in not just GR but just about every area of physics. You don't realise the vastness of material that exists on it, making up probability millions of man years of research! You have no first hand experience so you assume that if you just ignore the issue of such things as the North pole problem for a sphere then you're okay. Wrong. Its a common mistake to think that something you haven't is easy. Do you think its just a matter of "surjective okay, injective bad!"? Do you think that everyone in the last few hundred years of research into non-Euclidean geometry and manifolds has been compartmentalising their research so that they don't remember 'injective' and 'surjective' when doing coordinates? That no one during their research managed to recall two of the most common concepts in mathematics and what role they might play in mapping between spaces?

I'd say false. To a first approximation for a small mass falling towards a big black hole then its true but if the in falling object is of comparable mass then no. The Einstein Field Equations are non-linear, you can't object the space-time for 2 objects by working out the space-time for each object individually and then summing them, else mutually orbiting black hole decays would be easy. Most astronomical systems are sufficiently close to the small mass approximation to be good enough. In the world of quantum gravity that isn't the case. Prometheus and I happen to have done work in this area (not together). I did work which looked at how a 7-brane sat in the background space-time generated by an infinite stack of 3-branes. To first approximation you can work out a gravity dual to the mass gap and chiral symmetry breaking in QCD-like theories and when you add in a back reaction due to the 7-brane no longer being 'a probe' you get Goldstone modes associated to the broken symmetry.

You're on our home turf telling us our business despite the fact you have never been in this business or anything close to it. There's no shame in saying "I was wrong" or "I don't know" but you seem to have dug yourself deeper because of your unwillingness to say it. But like I said, if you think we're all wrong feel free to write up your work and send it to a journal, see what they say.

16. ### RJBeeryNatural PhilosopherValued Senior Member

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Chapter 7...
OK this is interesting...by this do you mean 2 grids with differing pole axes? So you're saying you could use one grid for all areas except the poles, and for those you would use the other grid? Sounds to me like the same thing as adding the "point of infinity" as you mentioned. Unless there is a way to specify each point using "both grids" or something?

I frankly still don't see the problem with a surjective coordinate system describing reality. I see this the same as listing another dimension (say, q) for a point on the xy plane. Any or all q will do and the point itself is not "in doubt" (x,y,q=any of infinite values). This doesn't make that point's existence difficult to accept. And I know it's frustrating to you that I value common sense when interpreting reality, but I DO have a problem accepting an injective coordinate system in describing that reality. I reject the EH for the same reason many Physicists reject the Singularity. It's called REALity, after all, and if we cannot describe it mathematically then it simply doesn't sit well with me.

All Physicists speak like the Hulk, right?

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Maybe you can do these things for me:

1) Describe a physical object whose existence no one can deny (such as a sphere) which can be described mathematically only in terms of an injective coordinate system.
2) Describe the BH/EH we've been discussing with a coordinate system other than an injective one.

If you could do this I would certainly learn something and admit it.

You said
but I've looked and looked for the link without success. Could you please give the reference again? Even when I don't find your comments helpful towards the OP I still find them occasionally interesting.

=======================================================
Completely setting aside all math lessons above (the whole surjective/injective/bijective coordinate issue is a secondary argument), let's discuss the following.
Black holes do not spontaneously come into existence. A mass undergoing gravitational stress sufficient to create a black hole does so at the center first between 2 atomic masses.

I'll change my tone. I'm not going to ask you to accept that these atomic masses never get close enough to create an EH from an outsider's perspective (even though that's what your comment above suggests to me), I'm going to ask that you admit that there is a "layman's common sense" reason for me believing that they never would. Is that fair?

And please stop acting like I'm insisting I'm right. Let me remind you...

17. ### Guest254Valued Senior Member

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This is becoming more and more cringe-worthy by the minute!

18. ### AlphaNumericFully ionizedRegistered Senior Member

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If you remove a point from a sphere then it can be 'unfurled' into a disk of infinite extent, aka a plane. Without that point removed you have to 'rip' the sphere to flatten it out. Hence a sphere can be covered everywhere but a single point using only one set of coordinates. To have a description of everywhere on the sphere you need a second set of coordinate over a region which once again is no more than the sphere minus a point. In regions where these two coordinate sets overlap they must be convertible into one another.

This is not the same as adding a point at infinity for a plane because it doesn't change the topology of the space. Coordinates are arbitrary descriptions of a space, they do not define or alter the space any more than describing an object in French rather than English alters the object being described. Adding or removing points alters the topology and can have enormous effects on the resulting system. The reason it 'sounds to you' like something else is because you have no experience with it or 'something else'.

Try doing some physics and finding out.

You said in another thread you're literate in 8 computer languages so maybe an analogy would help. Saying "What does it matter?" for this is like a programmer saying "Why don't we treat NaN like a number?". At first glance you might think its okay but you end up with inconsistent arithmetic if you do.

That's altering the space. A 2-sphere is two dimensional. Besides, adding in points or lines or whatnot, if done incorrectly, can be very very bad. For instance, a canonical example of a space which is not Haussdorf (which is a property manifolds have) is the real line with a double point at the origin.

You don't realise just how much formal mathematics is used in physics, or at the very least in the development of the tools used in physics. Once you start casting away what might seem innocuous properties you run the risk of pulling the carpet out from under you. Yes, some people do do work on spaces which aren't manifolds, which don't possess 'usual' properties like commutative geometry but they get up to their necks in extremely detailed mathematics because they're tinkering with the foundational core of what most physicists take for granted. I don't think most physicists even know what 'Haussdorf' means, yet its a property every single one has used implicitly.

This isn't about common sense, common sense goes out the window when you get down to the fundamentals of physics and mathematics. And you make it sound like physicists are slaves to mathematics or logic and don't use any other kind of critical evaluation. I know you want to think you're coming at things from some novel angle but the fact is you're completely unaware of what is involved in even building the tools physicists use, never mind extending them into new areas.

How much experience do you actually have using various coordinate systems on non-Euclidean spaces? On what are you basing your 'common sense'? Euclidean geometry? High school calculus? Programming arrays into computers? None of them prepare someone for the sorts of mathematics used in differential geometry, at least not any more than introducing them to the simplest of concepts involved. If 'common sense' is "I expect new things to behave like old things" then common sense is a poor guide. If common sense is "In mathematics I will assume physically motivated things" then common sense is a poor guide. 'Common sense' says parallel lines don't meet but then 'common sense' people have is developed in an everyday world where everything is Euclidean. The world of the very big or very small isn't so simple. 'Common sense' says that if A sees B going at speed v and B sees C going at speed w then A sees C going at v+w. That's what everyday experience leads people to believe but the world of the very very fast isn't so simple.

I find cranks like to play the "I might not have a formal education but I have a brilliant intuitive grasp of how the universe works!" role, particularly when talking to me. Invariably thought what they actually do is assume the universe is, on all scales, much the same as everyday life. It isn't. And you'd know that if you bothered to find out rather than asserting things you know nothing about.

Then your reason is demonstrably wrong. All physical quantities are finite on the horizon. Causality is preserved, coordinates can be defined, conservation laws apply. You have a reason but don't delude yourself into thinking its anything other than "I don't understand it so its wrong".

So you want me to describe a space which is not globally equivalent to Euclidean space? Spheres, tori, Möbius strips, annuli, anything which is not simply connected or contractable. Manifolds are spaces which look like flat space close up but globally they can be quite different. Pick your favourite non-Euclidean manifold.

You can also make nice spaces bad. For instance, define $\phi : \mathbb{R} \to \mathbb{R}^{2}$ where the image does 'loop the loop'. This means there's a pair (a,b) such that $\phi(a)=\phi(b)$. This means the image $\phi(\mathbb{R})$ is not a manifold, even though $\mathbb{R}$ is. Its the reason a Klein bottle is a manifold but its representation in 3 dimensions is not, it self intersects.

Actually if you construct the Penrose diagram for a Schwarzchild black hole you find that the region of space covered by the Schwarzchild coordinates is not the entire story, there's a second asymptotically flat region. The only way to examine it is through the use of several coordinate patches, allowing you to move through the event horizon in a certain way. Therefore you cannot use the Schwarzchild coordinates to describe every point in the manifold, they are not injective or surjective.

You obviously have no wish to learn else you'd have done some yourself, rather than simply assuming your naive conclusions are correct until someone tells you differently.

http://en.wikipedia.org/wiki/Aharonov-Bohm_effect

Your question mentioned an event horizon, you explicitly stated that the black hole had already formed. And atomic masses are never high enough to form black holes gravitationally.

I understand what you're saying but for all intents and purposes it would. A distant observer watching say two neutron stars collapsing together into a black hole would see them close down more and more and the light get more and more red shifted. As the time dilation becomes more and more pronounced the red shifting does too, though the collapse slows down from the observers point of view. As such the system gets dimmer and dimmer, colder and colder. Eventually the thermal emissions (which are used to observe the system) become swamped by the CMB and system cannot be observed in any meaningful way.

This is further enforced when you consider the point of view of someone who then falls into the black hole. Someone falling into a black hole will experience the event horizon and will be able to work out when they cross the EH by the view of the stars around them. Suppose they start flashing a light back to the person outside. A distant observer will not see the infalling person flash their torch ever. Anything which any infalling object or person does once they pass that surface will be unobservable. The haze of slowly moving in falling objects a distant observer sees around a black hole will only ever provide the distant observer with information on what those objects did before they reach a certain distance from the core (ie the EH). The common notion of a black hole being some kind of black sphere in space is not quite accurate as the infalling objects form a swarm around it. However, its still black in the sense nothing ever comes up out of it which wasn't there when the black hole formed. By that I mean that the two neutron stars do know and see the event horizon form around them, as they were within it when it occurred. A distant observer can deduce the event horizon size either by measuring the space-time metric and EM fields on a sphere enclosing the black hole (ie determining the Bondi mass) or by noting the largest sphere which is below all infalling objects.

Collapsing dust systems to form black holes is a common area of research, its not something people haven't considered. I wouldn't be surprised if, when you crunch the algebra, you find that although the time dilation makes the collapse seem slower it does form an event horizon, from the point of view of an outside observer, in finite time. In other words the collapse speeds up more than the time dilation slows it, from the point of view of a distant observer, and the process is finished in finite time. And even if it isn't the difference between the hypothetical 'completed' black hole and a 'not quite formed from the point of view of a distant observer' black hole is completely unmeasurable in any astronomical experiment.

19. ### RJBeeryNatural PhilosopherValued Senior Member

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Good response, AN, thanks; I learned quite a bit. You either are or will be an excellent instructor (except maybe for the parts where you keep telling the students how stupid they are

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).
Point of clarification here. I asked for something tangible which can ONLY be described in terms of an injective coordinate system. I can describe Spheres, tori, Möbius strips and annuli with surjective coordinates. It might not matter because...
It sounds like I misunderstood the definition of injective coordinates. My current understanding is that Schwarzschild coordinates are injective on this manifold because there exists "at most, one" coordinate set for each point on that manifold. I considered an "indeterminate" point, such as the EH, to have ZERO coordinate sets describing it (which qualifies as "at most, one"). It doesn't matter, because if the BH is unable to be described by ANY single coordinate system this just raises the bar even higher. I'm even more certain no one can provide an example of something tangible which can neither be described with injective nor surjective coordinates.

It's all moot, AlphaNumeric, I'm finished with the subject. You were among the more mature responders and clearly the only real authority on the matter. I think the following quotes summarize the thread:

We'll call it differing interpretations of a currently unfalsifiable premise.:scratchin:

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*facepalm*

21. ### RJBeeryNatural PhilosopherValued Senior Member

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Prometheus, rather than acting like a douche-bag why don't you explain the difference to me? An injective coordinate system does not need to be able to map to every point on its codomain. Is the EH considered to be outside of the codomain? How can that be? As I said, it only raises the bar and strengthens my argument, but I would like to understand, nonetheless.

22. ### AlphaNumericFully ionizedRegistered Senior Member

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You're wrong in how you understand it. A given coordinate chart will associate part of the manifold with part of a Euclidean space. If its a good chart then on that part of the manifold it provides a bijective map to the part of Euclidean space. The reason I said 'open sets' in my more formal definition was because that's how you formalise that, a sphere is a closed set but charts are defined automatically on open sets and thus cannot cover the whole of the sphere in one go, thus making their bijective property much more natural.

For every point which isn't a physical singularity there exists infinitely many different charts. Not every chart you can think of is a valid chart for a given open subset of the manifold. The Schwarzchild chart is not a valid chart if your subset of the manifold includes the event horizon. However, if your open chart contains the event horizon you can choose from a set of charts which includes the Kruskal or Eddington-Finklestein charts. The EH has infinitely many valid charts definable on it.

You never got started, so you can't 'finish' with it. You've just demonstrated you never even understood what a chart was yet you're daft enough to think you can tell people how they work and you've got insight into it others don't?

You want to pretend you're guided by common sense and you're being rational but you're not. You assert things on topics you don't understand, refuse to acknowledge you don't understand and you try to tell people their business. When Dinosaur explained pseudo-random number generators to you you explained how you are literate in 8 computer languages, demonstrating you don't think people should tell you your business but you're a hypocrite because you do that to others.

Which has nothing to do with your attempts to assert things about coordinates, manifolds and injective maps. Have you realised you're in over your head and now you want to back out using the excuse the original point has been addressed? You brought up something which you've been demonstrated wrong about and you want to avoid admitting it.

23. ### prometheusviva voce!Registered Senior Member

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AN has already explained this better than I could so I won't bother adding my own understanding to the melting pot. I will only add this; AN called you a hypocrite and he's right, but this excerpt makes me think you're not only a hypocrite but a filthy liar:
You don't really want to understand, you want people to look at your posts and think "ooh, he's clever," when in reality you've done none of the things required to form opinions on the things you're pontificating about. Much like the quite ridiculous member title you've given yourself - you're not a physicist, armchair or otherwise and it's an insult to genuine physicists that you claim that about yourself.

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