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Hawking radiation , black hole size

  1. Dec 26, 2012 #1
    Hi.

    If the hawking radiation is emitted from outside the event horizon , because probably that's the last place where the particles are being able to escape, then how come huge black holes ever evaporate as the matter behind event horizon has no chance of escaping in any way as to the immense gravity but as the matter is constantly building up inside the black hole and it's getting larger and larger sucking in more and more , then space should be one giant black hole after some time?
     
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  3. Dec 26, 2012 #2

    mfb

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    What do you mean here?
    If there is no matter or radiation flowing in, black holes do not grow.
    Hawking radiation gives some an extremely low temperature (for stellar and galactic black holes), so they emit some radiation and lose energy in the process.

    Currently, this temperature is below the temperature of the comic microwave background (CMB, 2.7K), so all black holes (at least all known black holes) grow as more CMB radiation flows in than Hawking radiation leaves.
     
  4. Dec 26, 2012 #3
    Yes I understand that black holes don't just grow themselves but they pile up the matter that get's behind the event horizon , so this is what I meant that how come they be just a infinitely small point if there is actually matter going inside it all the time and not coming out.
    That means they must grow in physical size or if not in size atleast consume more and more matter and so expand and consume even more as some mater get's in their way and given the huge lifetime of our universe how come we aren't one big black hole yet?
     
    Last edited: Dec 26, 2012
  5. Dec 26, 2012 #4

    mfb

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    There is nothing which could hold infalling matter back, so it just follows gravity towards the center.

    However, this does not mean that everything falls into a black hole. It attracts other masses, but so does every mass in the universe. The sun (and every other star) attracts all other objects in the galaxy, too. So what? Some objects (like earth) orbit the sun, and other objects do not care at all because they are so far away that the gravitational attraction is negligible.
     
  6. Dec 27, 2012 #5
    Remember that although the black hole gets bigger, it still obeys the law of gravity which means that the gravitational pull weakens exponentially with distance. Eventually after it consumes everything in a certain proximity of itself, the other "close" objects will be bound to a stronger pull from other objects

    As for size, I can't remember why it doesn't get bigger and bigger forever.
     
  7. Dec 27, 2012 #6

    mfb

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    It is not exponential. Unless you are really close to the black hole, it follows the usual 1/r-potential, which gives a force proportional to 1/r^2.

    It does not consume everything in its proximity. If you would replace sun by a black hole of the same mass, for example, all planets would just continue to orbit it.

    There is a limited amount of mass falling in.
     
  8. Dec 27, 2012 #7
    1/r^2 is a exponential equation. Hense the exponent.


    And your "proving me wrong" about black hole absorbsion of objects within a certain proximity actually proves me right. Your example of a black hole consuming the sun shows that your theoretical black hole absorbed something in a certain proximity and left other objects alone. That's exactly what I explained. Not sure where the confusion is there. If its that I said the other objects would be bound to other gravitational pulls, I was simply using a single case for an example. Your example would be another case and there are probably many more we clould come up with but as long as the OP understands the conveyed concept I think it is sufficent to use one case. Thanks for the reply though.
     
  9. Dec 27, 2012 #8
    1/r^2 is an inverse square law. 2^r or e^r would be exponential, which it is not.
     
  10. Dec 27, 2012 #9

    Nugatory

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    Nope, it's polynomial, not exponential. If it were of the form ar then it would be exponential.

    I think you may have misunderstood mfb's point. He was saying that the black hole does not consume everything within a particular distance; indeed, nothing outside of the black hole, no matter how close it is, cares whether it's in the vicinity of a black hole or just a normal very massive body. What does matter is whether the worldline of the object in question intersects the event horizon; if it does, the object falls into the black hole and if it doesn't the object doesn't fall into the black hole. Either way, the proximity is irrelevant; you can come very near on a high angular momentum trajectory and escape the black hole, or fall into it from infinity on a low angular momentum trajectory.
     
  11. Dec 27, 2012 #10
    Yikes, apparently the use of the word proximity is not sufficient here. I will surely be more careful with my wording on PF. I am spending more time explaining my words in deeper detail than I am learning.

    Also I must be wrong with many others on the inverse square law being non exponential because a simple search shows that many people think it is.

    http://www.britannica.com/EBchecked/topic/242523/gravity/61489/The-inverse-square-law#ref210893

    http://lofi.forum.physorg.com/Newton-And-Inverse-Square-Law_24364.html [Broken]
     
    Last edited by a moderator: May 6, 2017
  12. Dec 28, 2012 #11

    mfb

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    That was not my example.

    For a black hole with 1 solar mass, this proximity is ~10 kilometers - which is extremely small on astronomic scales. There are stable orbits with a radius of just 10 kilometers. If it is rotating (and all known black holes are rotating), that distance gets even smaller.

    Many wrong others do not make it right. You first link is not an example of this, however.

    Read carefully: If the gravitational field (more precise: gravitons) had mass, the potential would be exponentially (and not an inverse square law!). This is known as Yukawa potential, and appears in the attraction between nucleons, for example.

    http://xkcd.com/386/
     
    Last edited by a moderator: May 6, 2017
  13. Dec 28, 2012 #12
    So your saying "mfb" that if there is a planet "A" a distance of 100 000 km away from star "B" then the gravitational pull is let's say "G"

    Now star "B" burns up all hydrogen explodes and the left over mass forms a black hole, And the gravitational pull between that newly formed black hole and the planet "A" would still be "G" ?

    Or it should be less than "G" because while the star was in i's active life it had more mass as it used some of it and radiated that away as energy, and when it goes into the gravitational collapse/runaway fusion explosion stage it emits even more matter traveling away and after forms a black hole if I understand correctly, as a black hole can be created only if no fusion energy is left to counteract the gravitation?
    So is the "g" the same or not?
     
    Last edited: Dec 28, 2012
  14. Dec 28, 2012 #13

    mfb

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    To maintain fusion, the star has to be so big that no planet can orbit it at a distance of 100 000 km. Well, this number does not matter, we can just take 1 billion km.
    The mass of a star slowly decreases during its lifetime - and decreases even more if it ends in a supernova. As a result, the mass of a black hole (if it forms after the supernova) is lower than the mass of the previous star - if a planet survived the supernova, it will probably increase its radius a bit. Gravitational attraction at a fixed distance is proportional to mass, so the gravitational acceleration at the same distance decreases, too. I don't see the relation to the topic here.
     
  15. Dec 28, 2012 #14
    Well ofcourse I made those 100 000 km just for the sake of analogy not actual fact.

    By the way you said quote: "There is nothing which could hold infalling matter back, so it just follows gravity towards the center."

    Isn't there any chance of some matter having a very high rotational velocity around the BH before event horizon that the tangential velocity becomes so high that the matter escapes the BH?
     
  16. Dec 28, 2012 #15
    Outside of the event horizon? Absolutely, outside of the event horizon a black hole acts just like a normal object with the same mass. This is what mfb was saying: if you replaced the sun with a black hole of equal mass you wouldn't notice any change gravitationally.

    The second you are past the event horizon though, no matter how large your tangential velocity is you can't escape.
     
  17. Dec 28, 2012 #16

    Nugatory

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    If the star loses mass, then the strength of its gravitational field will be less after the mass is lost. This is because the strength of the gravitational field depends on the mass; it doesn't matter whether the star collapses into a black hole or not.
     
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