2
$\begingroup$

We know how to define black holes as trapped surfaces and solutions from gravitational theories. However, if we define black holes as vacuum solutions/charged solutions to Einstein Field Equations, can we have a well defined black hole interior? Classically, it seems not be problematic unless you realize time-like coordinate flips after passing the black hole horizon.

Do we know if black hole interiors are vacuum too? I ask this because, e.g., there were some trials to define rotating black holes as fluids of some type but it failed as far as I know. So, is black hole well-defined after all? Is it "matter"?

Improve this question
$\endgroup$
3
  • $\begingroup$ well defined black hole interior What do you mean by "well defined" ? $\endgroup$
    – StephenG - Help Ukraine
    Commented Oct 28, 2021 at 20:24
  • $\begingroup$ You seem to confuse two things here: vacuum solutions of EFE, and their associated interior solutions used to model "stars". $\endgroup$
    – Jeanbaptiste Roux
    Commented Oct 29, 2021 at 8:15
  • $\begingroup$ The mathematical definition of a black hole has nothing to do with trapped surfaces. In lay terms, you define it as the portion of a given spacetime that cannot send information to null infinity. $\endgroup$
    – Filipe Miguel
    Commented Oct 29, 2021 at 14:40

1 Answer 1

Reset to default
1
$\begingroup$

A time-line coordinate flips, only if one assumes that Schwarzschild's vacuum solution is valid in the interior of black hole, too. In my view, it is not correct. A solution of Einstein field equations spans the whole spacetime. In case of compact mass it can be cast into two parts: the interior and the exterior one. It is admissible to work with only one of them, and glue it to other, but it is not admissible to extend them over their validity domain. Possible, there is no interior spacetime at all. See for example Aharon Davidson's paper entitled 'Hollowgraphy Driven Holography: Black Hole with Vanishing Volume Interior' https://arxiv.org/abs/1007.1170, or t'Hooft lecture https://webspace.science.uu.nl/~hooft101/lectures/GtHBlackHole_latest.pdf, where he introduced his idea of vacuole on page 42. I believe to have proved that within the framework of classical general relativity.

Improve this answer
$\endgroup$

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.