Black Holes & Infinity(Singularities)

  1. Aug 4, 2014 #1
    Hello. I would like to know. Does matter when heading towards a black hole then crossing the
    event horizon threshold reach the speed of light? I am guessing no. It simply crosses the threshold
    and at a finite velocity heads toward the center of the blackhole.

    The escape velocity of a black hole I believe is something greater than the speed of light. Has anyone actually calculated what that number is?

    What is a Singularity? I only believe that matter simply reaches the center of a blackhole.
    Where in the world does infinity come from?

    Thanks for any and all responses
  2. jcsd
  3. Aug 4, 2014 #2


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    Gold Member

    I'm not sure on this one, but I think you have it right.

    Why do you think it is greater than c? I've never heard that before. The event horizon is DEFINED as being the place where the escape velocity is c.

    Singularity: a place where our math models give results that can't possibly be real, so we say that the model has broken down. We we abbreviate the aforgoing sentence by just saying "singularity"
  4. Aug 4, 2014 #3
    No. Nothing with any mass can ever reach the speed of light; it can only approach it and suffer mass gain and shortening.
  5. Aug 4, 2014 #4


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    Staff: Mentor

    Reaches the speed of light relative to what? As far as the falling object is concerned, it's at rest while the black hole is moving towards it (have you ever tried skydiving and experienced the earth "rushing towards you"?). A distant observer will find that the speed of the falling object relative to the observer approaches ##c## as the object disappears into the black hole. If the infalling object emits a flash of light in any direction at any time during its fall, the flash of light will move away from the object at ##c##.

    There's no meaningful definition of escape velocity once inside the event horizon. No matter what direction you move, no matter how far and fast you move in that direction, your path will lead to the central singularity. Although....

    The infinity is just an artifact of the math. For a more intuitive example, we could consider the classical formula for the force between a positive-charged and a negative-charged particle: ##F=kQ_1Q_2/r^2##. It works just fine as long as ##r##, the distance between the two particles, is not zero, but blows up to infinity if ##r## is zero. That's a singularity, but all it really tells us that you can't separate two charged particles by zero distance. A similar singularity appears if we set ##r=0## in the Schwarzchild equation that describes a black hole, and again it just tells us that that's not the right formula to use there.
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