4
$\begingroup$

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.

$\endgroup$
3
  • 1
    $\begingroup$ To my knowledge any star that exceeds some critical $M/R$ ratio becomes a black hole. Its formation starts with diverging pressure at the center by finite energy density. In case a known solution (metric) the critical ratio is defined by $g_{00}(0,M/R)=0$. $\endgroup$
    – JanG
    Commented Oct 22, 2022 at 14:43
  • $\begingroup$ Jan Gogolin: Yes, I think that is the conventional wisdom in the field. But can you point out to a paper or a book where this is worked out for a specific model, apart from the dust bowl model ? $\endgroup$ Commented Oct 23, 2022 at 12:31
  • $\begingroup$ Pascal: Unfortunately not. I am looking for it, too. Pressure, understood as a mean hydrostatic stress, plays crucial role by forming of initial (central) event horizon. That can be seen on example of Schwarzschild's interior (static perfect fluid) solution. $\endgroup$
    – JanG
    Commented Oct 23, 2022 at 14:58

1 Answer 1

1
$\begingroup$

In numerical relativity, quite a bit of work has been done on exploring the threshold of black hole formation from gravitational collapse using different matter models. See here for a review article. It turns out that there are surprising phenomena that occur right at the threshold.

These simulations have been done for a large number of matter models, including perfect fluids, which may be relevant for your interests.

$\endgroup$
1
  • $\begingroup$ This review article definitely looks relevant, thank you! If others know of some other relevant work (numerical or analytic), they are welcome to post it here as well. $\endgroup$ Commented Oct 26, 2022 at 19:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.