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Graphical example of BH formation by PAllen

  1. Aug 28, 2012 #1

    zonde

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    I liked this graphical example of black hole formation posted by PAllen in another thread and I want to discuss it.
    It is not unusual that arguments defending existence of black hole go like that:
    1. Assume that BH exists.
    2. Then observer falling into BH ...
    I think that point 1. is begging the question fallacy. So any argument defending BH should be about formation of BH.
    Therefore I think that this example of PAllen is excellent basis for discussions around black holes and so it is worth a closer look.

    Now about example. Let's say that we are looking at star at the far edge of collapsing cluster. Let's assume further that we have idealized situation where light from that star is going exactly through the cluster's center of mass. That particular star will be gravitationally lensed (amplified) and it is a bit unclear if it will be redshifted or blushifted as it is moving toward us not away from us, right?

    Another point is where exactly formation of event horizon starts? It does not appear at once but is expanding from some point by engulfing mass. So we have to have some seed black hole that is produced in collision of two stars near cluster's center of mass, right?
     
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  3. Aug 28, 2012 #2
    Yes, its an interesting scenario. If the distribution of stars is uniform, then r = 2m will first occur at the centre. But in a uniform sphere the gravitational force is strongest at the perimeter and weakest in the centre, so one might expect to first see the density increasing away from the centre.
    The normal scenario for black hole development is a collapsing massive star, after it has exploded a lot of matter away. This version has been simulated on computers and is well known. But is the collapsing star cluster really any different? Essentially it is a lumpy cloud of gas, but because of the lumpiness it has no pressure, and so is very similar to the Oppenheimer-Snyder calculation. Why would stars give a different result to particles of gas in a cloud of similar size?

    Mike
     
  4. Aug 29, 2012 #3

    pervect

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    In my opinion, the primary purpose of PF isn't to "defend" modern physics, but to explain it to those who are interested.

    The idea that we "should" explain in detail how a black hole forms may sound appealing , but it's rather unrealistic, requiring advanced knowledge. For pedagogical purposes, it's a disaster.

    For those who might be interested, some aspects of this hard problem are discussed in http://arxiv.org/abs/1010.1269. http://relativity.livingreviews.org/open?pubNo=lrr-2008-1&page=articlesu11.html [Broken] is also intersting.

    This is well, well, well beyond naieve and ultimately ill-founded arguments by non-experts who don't understand why black holes are thought to exist.
     
    Last edited by a moderator: May 6, 2017
  5. Aug 29, 2012 #4
    I agree. Though I'm not s sure everyone agrees with the part about "defending" not being the primary pupose of PF. See i.e. the rest of your post :wink:
    This seems to contradict your first paragraph, I'm not sure if you're for or against explaining, or just prefer explaining but only those subjects you think are easy to grasp for the average non-expert. But there are a whole lot of threads in PF that deal with just as hard or even harder (this is very subjective) issues like a brief look at this subforum or the Quantum physics, or HEP or condensed matter one.... shows, and I'm sure there is always some group of people that benefits from them depending on their background and intelligence. So why is that a pedagogical disaster?

    Right, that is why a forum like PF can improve IMHO even if it's just a little, those non-experts understanding of why BH's are thought to exist.
     
  6. Aug 29, 2012 #5

    PAllen

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    For pedagogical purposes, I think the Oppenheimer-Snyder collapse is reasonable for this highly idealized scenario.

    It is, in fact, known that GR predicts the event horizon to form at the center and grow. It is not true that some specific collision at the center produces it - the whole accumulation of matter produces it, without need for collisions (though, of course, they will happen). However, by definition, a distant observer never sees light from (or inside) the horizon at any stage of its existence. What you do see is the light from just outside the growing horizon, barely staying ahead of the horizon. Think about any period well before BH formation. You see newest light from the near edge, older light from the center, oldest from the far edge. For now ignore the issue of light from the far side of the cluster. At each moment you see light from the nearer stars down through the center, at some small time before the horizon has reached that point. A moment later, you see light from closer to when the horizon reached each distance. Then closer yet. Thus, the image is one of all the stars seeming to slow down (e.g. if you had a few binary systems thrown in, they would slow down their period) and redden collectively, until they become invisible by virtue of the highest energy gamma rays being red shifted to below CMB frequency.

    As for the stars on the far side of the cluster, I am not sure. Some mixture of blocked light and refracted light would seem likely. This part of the scenario would require careful simulation that would be a major project to perform (and I haven't bumped into any published simulations covering close to this situation - that of the optics of the stars of the far side of a collapsing cluster with no net angular momentum).

    The final result would look something like this:

    http://commons.wikimedia.org/wiki/File:BH_LMC.png
     
    Last edited: Aug 29, 2012
  7. Aug 29, 2012 #6

    PAllen

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  8. Aug 29, 2012 #7
    I have just been in touch with Saul Teukolsky, who has been doing simulations involving naked singularities, and his comment was

    "A naked singularity would be one not screened by an event horizon. There is no example yet of a naked singularity being generated by the collapse of non-exotic matter in a generic way. But it is also true that there is no theorem that rules it out. This has been the situation for over 30 years, so it's a hard problem. Because all the attempts to make a naked singularity have failed, most experts think you can't do it, but that of course is a psychological statement.

    Our work showed strong numerical evidence that you could make a naked singularity by collapsing matter that only interacted gravitationally. However, it was not generic, because the situation we looked at was perfectly axisymmetric. In any event, if you collapse an ordinary star and GR is correct, you definitely get a black hole with an event horizon."

    Mike
     
  9. Aug 29, 2012 #8

    zonde

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    I don't understand. As I see it "defending" is part of "explaining". To explain means to show how to come to certain conclusion so you want to show why other alternatives are untenable, right?


    I will get to the rest later after I will look at the links.
     
  10. Aug 30, 2012 #9

    PAllen

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    I've thought about the question of stars from the far side of the cluster more. I think I see the answer. Each wave front from the cluster you see from afar will have images of the far side of the cluster closer and closer to the last point when light from the far side will cross the center. Over time, the last light you will see from the far side approaches light reaching the center at the moment the event horizon forms and starts growing. The net result is that there is no unusual change in the appearance of the cluster from afar - you always see the whole cluster as of different points in time. It reddens and disappears, but you never see anything that explicitly confirms an event horizon (as opposed to deducing it).
     
  11. Aug 30, 2012 #10

    zonde

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    The more advanced are the arguments the more error prone and harder to check they are. So less believable is the claim.

    Okay, but it has to start at some point. And that point can't be just empty space. Next in order for it to grow it must accumulate more matter i.e. collide with it.

    We should see the light from the far side star that bends around mass center. So it seems that this star should turn into Einstein's ring before disappearing.
     
  12. Aug 30, 2012 #11

    zonde

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    I suppose that we can draw some analogy with gravitation potential of Newton's gravity and gravitation potential is lowest at mass center even as gradient of potential approaches zero. And black hole should be born where gravitation potential is lowest. Hmm, unless some star at it's center has lower potential then center of mass.

    In case of stars we take degeneracy pressure into consideration. Not sure how to extrapolate it to cluster of stars.
     
  13. Aug 30, 2012 #12
    Yes, that's what I meant. In the cluster of stars there is normal pressure in each star, but due to the size of the cluster they are collapsing into a black hole without themselves collapsing into white dwarfs/neutron stars/whatever first. And there is no pressure between the stars as the black hole forms. So degeneracy just doesn't come into the pictrure.

    When they are all within the Schwarzschild radius, they are still well separated from each other (assuming uniform distribution).

    Mike
     
  14. Aug 30, 2012 #13

    PAllen

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    No, this is not necessary. The event horizon is just a surface of last light. There need never be any matter there. There are exact solution for a collapsing shell of matter that produce a black hole. In these, the event horizon starts as one point in the center. There is no matter at or near it when it forms.
    It would take simulation to answer this, so I can't be sure. However, my intuition is that this would happen for galaxies behind the collapsing cluster, but not much, if at all, for stars on the far side of the cluster participating in the collapse. I think the light from these stars emitted after the event horizon forms and starts growing simply never makes it out of the cluster.
     
  15. Aug 30, 2012 #14

    PAllen

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    This would relate to formation of the singularity, not the event horizon. The event horizon is a global phenomenon - it actually depends on the whole spacetime, including the indefinite future. For example, if you have a stable black hole and a baseball is going to fall into it next year, there is some photon so slowly 'escaping' that this future infall means it will never escape. Thus, this future event affects the location of the event horizon now.

    There actually need not even be light trapped at the event horizon. It is a theoretical surface defined by the escape to infinity, in infinite time, of null paths.

    One further consequence of the definition of event horizons is that for a closed universe, you cannot actually define an event horizon because there is no future infinity.

    There is a related concept of apparent horizon, which has a local definition, and is (almost always) inside the true horizon.
     
    Last edited: Aug 30, 2012
  16. Aug 30, 2012 #15

    PAllen

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    Exactly! That was the whole point of my construction. There is no limit to how low the density of a black hole can be, if you have enough total mass.
     
  17. Aug 31, 2012 #16
    The "trillion stars collapsing" scenario giving rise to a "blacker than the CMB" region, would be at least ideally and according to theory what we would observe if we had the chance to witness the formation of such a supermassive black hole. Now this hasn't happen yet and we probably won't ever see it as this supermassive black holes usually form in galactic bulges and represent a tiny fraction of the bulge or the AGN, so there is no way to discern from afar.
    So basically the only way we have to infer their presence is the tremendous quantities of radiation of different wavelengths they radiate from infalling matter accreted around the black hole.
    If a physically reasonable mechanism of production of that massive radiation was found, there would be real motives to seriously question the black hole paradigm IMO, this hasn't happen yet, at least that I know.
     
  18. Aug 31, 2012 #17

    PAllen

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    Yes, these are all valid observations. However, I thought the intent of the thread was to get at the frequently recurring questions of interpretation what GR says about black holes (separately from any questions about how strong the evidence for them is).

    The point of my admittedly absurd scenario of a trillion stars collapsing with no net angular momentum in a completely smooth way was to confront a common resistance to admitting the reality of the 'inside' of a collapsed object that comes from excessive focus on matter falling into a pre-existing perfect SC black hole. I think my scenario succeeded admirably in this.
     
    Last edited: Aug 31, 2012
  19. Sep 1, 2012 #18
    PAllen, I find this fascinating because it is so counter-intuitive (to me, at least!). Can you supply any references to articles discussing this?

    From a Newtonian perspective, the whole interior of a uniform shell should have the same gravitational potential and zero gravitational force.

    Mike

    Edit: I have read in many places that a black hole (and event horizon) only forms when all the matter is within its Schwarzschild radius!
     
    Last edited: Sep 1, 2012
  20. Sep 1, 2012 #19

    PAllen

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    No, it happens also when any subset of matter is within a critical radius (which, in realistic cases - the whole universe is not spherically symmetric around one collapsing mass, that has no rotation), which is not exactly the same as the SC radius. But that is all irrelevant - in the shell example: when the whole shell is within the SC radius there is still no matter at the center. You don't need anything to derive the properties of this scenario (for the spherically symmetric non-rotating case) beyond Birkhoff's theorem.

    Newtonian analog is not relevant - collapsing objects are the case when GR has maximum disagreement with Newtonian gravity. Even so, potential and force have nothing to do with event horizon. The event horizon (over time) is just 3 surface (2 space x 1 time) in the spacetime manifold from which no forward going null paths escape to infinity. So, as an object collapses (pretend it is transparent), there is a point where null paths from the center reach the outside only when the whole object is within the SC radius. Since getting from center to outside takes time (during which time the object is collapsing), rays from the center are trapped earlier than rays from the outside. This serves to qualitatively establish that the event horizon must grow from the inside out for typical collapse scenarios.
     
  21. Sep 1, 2012 #20

    PeterDonis

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    Actually, the EH is a null surface--more precisely, it has two spacelike and one null dimension. The third dimension has to be null for the EH to have the property you describe (which it does).
     
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