3 ms·

Imagine a cone with a fixed diameter for the base. That represents the black hole’s external event horizon. Now stretch the point of the cone away from the base

Imagine a cone with a fixed diameter for the base. That represents the black hole’s external event horizon. Now stretch the point of the cone away from the base... forever, as the singularity warps space time more and more. The volume of the cone (inside the event horizon) will grow as the point moves further away from the base.

pdonis 8y ago
Can you give a reference to a paper that describes the math behind this?
- raattgift 8y ago
  Neglecting evaporation, it's a lot closer to Yen Chin Ong's results (and those he cites, especially Christodoulou and Rovelli [2]) than most of the comments throughout this discussion, in that with a careful choice of time coordinate a spacelike spherical sector of a Schwarzschild black hole could evolve roughly similarly. Of course, one has enormous freedom to choose spacelike hypersurfaces through a Schwarzschild black hole, so such a result is not especially interesting without some sort of uniqueness proof for the idea, and I don't think that's achievable. (cf [2]). I'm also not sure this is what GP has in mind. - -- [1] https://arxiv.org/abs/1503.08245 https://arxiv.org/abs/1503.08245 (§ 2) (simpler overview: https://www.kth.se/profile/ycong/page/the-interior-volumes-of-black-holes https://www.kth.se/profile/ycong/page/the-interior-volumes-o... ) [2] https://arxiv.org/abs/1411.2854 https://arxiv.org/abs/1411.2854 (§ IV)
  - pdonis 8y ago
    Thanks for the references. The Rovelli paper seems to be the key one deriving the claimed result. I have to say the result looks contrived to me: they are constructing spacelike surfaces with increasing volume only by what I would call severe gerrymandering. But that's probably off topic for this discussion.
hn_throwaway_99 8y ago
Thank you! I think that's about the best possible layman's explanation that I could (in the weird world of trying to think in higher dimensions) understand.

pdonis 8y ago

Can you give a reference to a paper that describes the math behind this?

raattgift 8y ago
Neglecting evaporation, it's a lot closer to Yen Chin Ong's results (and those he cites, especially Christodoulou and Rovelli [2]) than most of the comments throughout this discussion, in that with a careful choice of time coordinate a spacelike spherical sector of a Schwarzschild black hole could evolve roughly similarly. Of course, one has enormous freedom to choose spacelike hypersurfaces through a Schwarzschild black hole, so such a result is not especially interesting without some sort of uniqueness proof for the idea, and I don't think that's achievable. (cf [2]). I'm also not sure this is what GP has in mind. - -- [1] https://arxiv.org/abs/1503.08245 https://arxiv.org/abs/1503.08245 (§ 2) (simpler overview: https://www.kth.se/profile/ycong/page/the-interior-volumes-of-black-holes https://www.kth.se/profile/ycong/page/the-interior-volumes-o... ) [2] https://arxiv.org/abs/1411.2854 https://arxiv.org/abs/1411.2854 (§ IV)
- pdonis 8y ago
  Thanks for the references. The Rovelli paper seems to be the key one deriving the claimed result. I have to say the result looks contrived to me: they are constructing spacelike surfaces with increasing volume only by what I would call severe gerrymandering. But that's probably off topic for this discussion.

hn_throwaway_99 8y ago

Thank you! I think that's about the best possible layman's explanation that I could (in the weird world of trying to think in higher dimensions) understand.