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Mass of a singularity

  1. Jul 16, 2006 #1
    In "Universe in a Nutshell" Stephen Hawking says that black holes have mass, and it is the mass of the original star + matter absorbed - hawking radiation in time, or something like it.

    Right, but: if a singularity has for definition an infinite density, this mean that it is the maximum density one can think, so why should mass change from black hole to black hole, if the density in a non-dimensional space is alredy the maximum?
  2. jcsd
  3. Jul 16, 2006 #2


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    Because you calculate the density as mass/volume; you do not calculate (in the case of a singularity) mass as density x volume.

  4. Jul 16, 2006 #3
    D= m/v; D=Infinite

    It means that: Infinite*v=m; -----> Infinite=m

    What is the problem with this?
  5. Jul 16, 2006 #4


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    mass = finite
    volume = zero

    density = mass/volume = infinite (a mathemetician might say undefined, because you are dividing by zero)

    mass = density * volume = infinity * zero (undefined!)

    The moral of the story is that division by zero is bad, and should be avoided.

    However, the mass of a BH is not undefined. To see this, go back to the original definitions.

    We can measure the mass of a black hole from outside the black hole, (by looking at its orbits a long way away and applying Keppler's law, for instance) - technically this requires that the mass of the black hole not be changing.

    So the problem isn't with defining the mass of the black hole, the problem is the idea of having a finite mass in zero volume. I.e. the problem is the infinite density.

    Quantum gravity will "probably" replace the zero volume of the singularity with some finite volume, but we don't have a theory of quantum gravity yet.
    Last edited: Jul 16, 2006
  6. Jul 16, 2006 #5
    Just a thing:

    s = v*t ; (v=0 ; t=infinite)

    s = 0*infinite = 0

    why you say it is undefined? in an infinite time a corp that moves at 0 speed makes 0 space.

    Isn't the analog case with m = density*volume = infinity*0 = 0?

    I just tried to say that in order that black holes mass changes, the density and the voulume cannot be infinite.
    I don't see why would be necessary to have a QG to understand what we have alredy....
  7. Jul 16, 2006 #6


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    there are some serious flaws in your logic... like the use of one sample to decide on a mathematical proof.

    For example, 3/0=infinity. So 0*infinity=3.

    But 4/0=infinity. So 0*infinity=4

    Here's a better question. If you divide 3 by 0, do you get positive or negative infinity?

    How can something be defined if you don't know whether it's the left most or rightmost extreme on the numberline? You can't get more divergent than that
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