I am looking for a paper that would study a mathematical model for the collapse of a star into a black hole (no QM please, just plain old GR). I know about the "dust bowl" model of Oppenheimer and Snyder, but I would like something slightly more realistic that takes pressure into account. For instance, there are the TOV (Tolman - Oppenheimer - Volkoff) equations, where density can increase with pressure. To ask a more specific question, is it known that for a star that's massive enough, the TOV model will lead to the formation of a black hole? Is it known that it does not lead to the formation of a black hole ? Or is that still an open question? Assuming spherical symmetry is fine if that helps.
Edit: Answers have been slow to come in, so I'll add a couple of words on what I would view as an acceptable answer. For models taking pressure into account, there's probably no exact solution (we do have the interior Schwarzschild solution, but it is static: no collapse here). However, it is often possible to study with rigorous math the evolution of a system even in the absence of explicit solutions. This is essentially what mathematicians working on differential equations, PDE, and dynamical systems in general do for a living, right?
In the absence of a rigorous mathematical analysis, a pointer to a paper presenting numerical simulations would be the next best thing.
