1
$\begingroup$

The Schwarzchild interior solution is a static solution with no singularity which can be coupled to the Schwarzchild exterior to obtain a static, singularity-free universe. How does this universe dodge the Hawking-Penrose singularity theorems? There is no exotic matter or anything like that, that I can see.

$\endgroup$
3
$\begingroup$

It is matched to the normal, exterior, solution at a radius greater than the Schwarzschild radius: thus there is no event horizon. So it is a (considerably idealised) solution that might describe something like a star, where the vacuum part of the field is the traditional Schwarzschild solution, but the field in the interior is not: consider the Sun, say.

$\endgroup$
6
  • $\begingroup$ And if it is matched to the exterior solution inside the Schwarzchild radius then there is an event horizon and then a singularity theorem does apply? Which means that the solution can longer be static and collapse is inevitable? $\endgroup$ Mar 1 '17 at 13:25
  • $\begingroup$ @DzamoNorton It can't be matched inside the horizon, it has terms like $\sqrt{1-R_S/R_m}$ in it, where $R_m$ is the surface radius and $R_S$ the Schwarzschild radus. $\endgroup$
    – user107153
    Mar 1 '17 at 13:34
  • $\begingroup$ Thank you @tfb. Last question! So when a real ball of dust collapses through R=2M it is forced to go from having (approximately) a Schwarzchild interior solution to having some other interior solution? $\endgroup$ Mar 1 '17 at 13:39
  • $\begingroup$ Ah, never mind @tfb. A collapsing ball of dust is not static so it never had the Schwarzchild interior solution to start with. I think the penny has finally dropped! $\endgroup$ Mar 1 '17 at 13:42
  • 2
    $\begingroup$ @DzamoNorton: a collapsing homogeneous ball of dust is described by the Oppenheimer-Snyder metric. $\endgroup$ Mar 1 '17 at 16:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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