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Spherical symmetric collapse of pressureless dust

  1. Jun 6, 2013 #1

    tom.stoer

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    Is there an exact solution for the spherical symmetric collaps of pressureless dust? Can one see a Schwarzschild solution for r > Rdust with shrinking Rdust(t) ?
     
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  3. Jun 6, 2013 #2

    Mentz114

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    It is possible to embed a form of the Friedmann solution inside an exterior Schwarzschild spacetime. I can't remember if the interior bit can be made pressureless. My only reference right now is Stephani's "General Relativity".

    [edit] The interior can be dust. So I guess this fits. This is the Tolman solution, it turns out.
     
    Last edited: Jun 6, 2013
  4. Jun 6, 2013 #3

    WannabeNewton

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    Assuming you are looking for the collapse of a uniform ball of dust, I believe what you want is the Oppenheimer-Snyder collapse: http://grwiki.physics.ncsu.edu/wiki/Oppenheimer-Snyder_Collapse

    See also if you can get access to Israel's paper on the collapse of a thin spherical shell of dust: http://adsabs.harvard.edu/abs/1967PhRv..153.1388I

    Eric Poisson talks about both of these things (Oppenheimer-Snyder collapse and thin shell collapse) in sections 3.8 and 3.9 of his text "A Relativist's Toolkit: The Mathematics of Black Hole Mechanics".

    Also, see the following passages from section 7.6 of Padmanabhan "Gravitation: Foundations and Frontiers":
    http://postimg.org/image/48aevjpkp/
    http://postimg.org/image/8swlah9a1/
    http://postimg.org/image/upj4aumgp/

    The rest of the section is about the nature of the collapse obtained from such solutions.
     
    Last edited: Jun 6, 2013
  5. Jun 6, 2013 #4

    tom.stoer

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    Great - thx!!
     
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