Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spherical symmetric collapse of pressureless dust

  1. Jun 6, 2013 #1


    User Avatar
    Science Advisor

    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) ?
  2. jcsd
  3. Jun 6, 2013 #2


    User Avatar
    Gold Member

    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


    User Avatar
    Science Advisor

    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":

    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


    User Avatar
    Science Advisor

    Great - thx!!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Spherical symmetric collapse of pressureless dust