Spherical symmetric collapse of pressureless dust

[tom.stoer]

Is there an exact solution for the spherical symmetric collaps of pressureless dust? Can one see a Schwarzschild solution for r > R_dust with shrinking R_dust(t) ?

 

[Mentz114]

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.

 

[WannabeNewton]

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.

 

[tom.stoer]

Great - thx!