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What density does something have to have to be considered a black hole?

  1. Apr 20, 2009 #1
    "Any amount of mass at all can in principle be made to form a black hole if you compress it to a high enough density."

    What is the high enough density?
     
  2. jcsd
  3. Apr 20, 2009 #2

    Nabeshin

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    Science Advisor

    This high enough density is the density at which the schwarzchild radius of the object is less than the actual radius of the object.

    Mathematically,
    [tex]r_s=\frac{2Gm}{c^2}=r[/tex]
    If you assume the object to be a uniform sphere, we can write its mass as the product of density and volume:
    [tex]m=\rho V=\frac{4/3}\rho\pi r^3[/tex]

    And substituting into the first equation,
    [tex]r=\frac{2G(\frac{4/3}\rho\pi r^3){c^2} [/tex]
    [tex]\rho=\frac{3}{8}\frac{c^2}{G\pi r^2}[/tex]

    In a completely classical universe.
     
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