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Can Black Holes Exist?

  1. Dec 26, 2009 #1
    The majority view in the physics community is that black holes not only can exist, but do exist.

    I accepted this for a long time, but I recently came across a website that claims black holes cannot exist and provides references to a great many papers on the topic that don't seem at all to be the typical crackpot/crank material. (I must point out, however, that the website author appears to be a bit cranky, in the sense of "irritable about the issue", although not crackpotty.)

    http://www.sjcrothers.plasmaresources.com" [Broken]

    Intuitively, I understand the argument to be this: It seems obvious that black holes can exist, because, when you keep adding mass to a large mass, at some point the force of gravity will be so strong that even light cannot escape the gravitational field. However, this ignores the expansion of space, and the accompanying dilation of time, that occur as more mass is "sucked in" to the prospective area of space where a black hole is to form. Formation of a black hole would require enough mass to get sucked in that Schwarzchild's radius would exceed the radius of the mass at the center of the black hole. This won't happen though, because as more mass is sucked, space expands, and you get a singularity, not a center, with a perpetually collapsing mass that perpetually exceeds its receding but growing Schwarzchild's radius. The radius is receding in the sense that it is getting further from the periphery of the black hole (think of a sphere in near flat space sufficiently large to contain the ever collapsing mass and expanding space). It is growing however, as more and more mass gets sucked in. This sounds paradoxical, but only because we are unused to the notion of expanding space.

    Of course, there is a small matter of mathematics involved.

    Here, Larry Abrams points to an error (he claims) made by Hilbert that led to the first black hole prediction and considers other ideas about black holes:

    http://www.sjcrothers.plasmaresources.com/Abrams1989.pdf" [Broken]

    Does anyone know of a refutation of Abrams' arguments or of any convincing argument that black holes must exist that attempts to address the criticisms made by the anti-black-hole people?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 26, 2009 #2

    atyy

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    Abrams's arguments are not explicitly refuted anywhere reputable, but they are not consonant with basic textbook understanding, which if you understand, will lead you to a refutation of Abrams's arguments. My recommendation is that it is generally a waste of time learning the manifestly wrong things in order to refute them (unless you want to be entertained). It is better to learn the basics well. Take a look at Ellis and Hawking's or Wald's texts.
     
  4. Dec 26, 2009 #3

    bcrowell

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    From your description, it sounds like their argument contradicts the Penrose–Hawking singularity theorems: http://en.wikipedia.org/wiki/Singularity_theorems It would be interesting to know whether (1) they think their argument contradicts the singularity theorems, or (2) they think it doesn't. If it's #1, they should state what error they think Hawking and Penrose made. If it's #2, they should say what they think is wrong with the standard interpretation of the singularity theorems.
     
  5. Dec 26, 2009 #4

    atyy

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    The two issues are different.

    Within general relativity, black holes do exist, and can be formed from realistic configurations of matter. This is not merely a "majority view", it is textbook knowledge.

    Whether black holes have been observed is a different issue. There are many candidates, but whether they are general relativistic black holes remains a research question.
     
  6. Dec 26, 2009 #5
    I learn better from reading and understanding papers than reading textbooks, probably because I enjoy getting to the bottom of controversies.

    Perhaps you can suggest a paper that establishes that black holes can exist, the simpler the better, because I am relatively new at this stuff. That may be the supposedly refuted Hilbert paper or may be some other paper that corrects for Hilbert's error (if he made one).
     
  7. Dec 26, 2009 #6
    What I meant by "black holes can exist" is that it is theoretically possible black holes can exist out there in space someplace. What I meant by "black holes do exist" is that there actually are black holes out there in space someplace. I see so many references to black holes being at the center of galaxies, etc., that I assumed that was the majority position, not that it much matters.

    I prefer to go directly to the papers that are the source of the textbook knowledge rather than the textbooks. Also, textbooks must be purchased. I'd rather find something available for free on the web. One thing I like about Crothers site is he makes so many original papers available. I guess I could start by reading Hilbert's, but I'm not sure that's considered a reliable paper generally.
     
  8. Dec 26, 2009 #7

    atyy

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    OK, have fun then!

    For a free textbook try, http://www.phys.uu.nl/~thooft/lectures/genrel.pdf [Broken]

    Footnote 8 will be of interest to you: "In his original paper, using a slightly different notation, Karl Schwarzschild replaced [mathematical expression, see the pdf] by a new coordinate r that vanishes at the horizon, since he insisted that what he saw as a singularity should be at the origin, claiming that only this way the solution becomes ”eindeutig” (unique), so that you can calculate phenomena such as the perihelion movement (see Chapter 12) unambiguously. The substitution had to be of this form as he was using the equation that only holds if g = 1 . He did not know that one may choose the coordinates freely, nor that the singularity is not a true singularity at all. This was 1916. The fact that he was the first to get the analytic form, justifies the name Schwarzschild solution."
     
    Last edited by a moderator: May 4, 2017
  9. Dec 26, 2009 #8

    bcrowell

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    There are three separate issues here: (1) whether there's a solution to the Einstein vacuum field equations with the properties of a black hole; (2) whether that solution is really reachable from realistic initial conditions; and (3) whether we actually observe black holes. Looking at the reasoning paraphrased in Thinkor's original post, it's clearly #2 that's the issue here. The material from t'Hooft's book is addressing #1. The Penrose–Hawking singularity theorems are what address #2.
     
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  10. Dec 26, 2009 #9

    atyy

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    Two more issues.

    1) How is the Schwazschild solution to be interpreted? The t'Hooft text I linked above is good but difficult. Easier texts are http://people.maths.ox.ac.uk/~nwoodh/gr/index.html [Broken] and http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html (I find Carroll's presentation of the mathematics impenetrable, but the physics chapters are good).

    2) However, the Scharzschild solution is an eternal blackhole, and cannot be formed by realistic configurations of matter. There is no easy source for this, and you have to see the singularity theorems linked by bcrowell above.
     
    Last edited by a moderator: May 4, 2017
  11. Dec 26, 2009 #10

    atyy

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    Yes, the OP text is about #2. The OP links to Crothers and to Abrams are about #1. And #3 is mentioned tangentially in the opening sentence of the OP.
     
    Last edited: Dec 26, 2009
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