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The article says 4+ dimension black holes can exist. Just curious about an oddball idea from complete laymen perspective - could a blackhole with a time dimensi

The article says 4+ dimension black holes can exist. Just curious about an oddball idea from complete laymen perspective - could a blackhole with a time dimension/component exist then? I'm sure someone's thought about that before me :)

seeknotfind 3y ago
Came to comment about the same thing. It's funny - higher dimension black holes can confidently exist in a model, but because the model isn't tied to reality, it's not a very meaningful statement. Time ends at black holes. They stretch out time infinitely, from an outside perspective.
- SanderNL 3y ago
  Time ends at black holes. Is it even possible to empirically validate such a thing?
  - BSEdlMMldESB 3y ago
    > Is it even possible to empirically validate such a thing? I wouldn't think so because empiricism implies experience which implies time
  - make3 3y ago
    only for outside observers... you can validate it if you go in :)
  - bmitc 3y ago
    I think what they meant by end is that time appears to stop at the event horizon for outside observers. As something approaches a black hole event horizon, time appears to infinitely slow, for an outside observer, such that a frozen image of the object gets stuck on the event horizon. But this image can't be seen because it gets infinitely red shifted such that no detection device can keep up with the longer and longer wavelengths.
  - GoblinSlayer 3y ago
    You can measure time dilation at different distances from black hole, then extrapolate and see that time dilation goes to infinity at the event horizon.
antognini 3y ago
Black holes already have a time component since they exist in a universe with 3-dimensional space and 1-dimensional time. The equations include both the spatial components and the temporal components. One of the curious features of black holes is that they reverse the roles of time and space in a sense. In ordinary space we have freedom to move around in space, but are constrained to only move forward in time. Different reference frames may move forward at different rates relative to us, but they always move forward. By contrast, once you pass the event horizon of a black hole, these properties swap. It's possible to "move freely" in time in the sense that you can find reference frames that appear to move backwards in time. But all these reference frames are constrained to move forward in space.
- Sniffnoy 3y ago
  The article explicitly says that it's talking about number of spatial dimensions, it's not including time. It says the new theorem shows that black holes can form into up to 7 spatial dimensions (plus 1 for time). (This isn't to say they can't form beyond that, just this new theorem doesn't show that.)
- Zamicol 3y ago
  According to GR, time stops at the event horizon. It would take infinite time to cross the event horizon. Everything past the event horizon is speculative.
  - magicalhippo 3y ago
    Not really. It just appears to take an infinite amount of time for an outside observer. For someone falling into a black hole, it takes a finite amount of proper time[1] to reach the event horizon. For that infalling observer, the horizon is a boundry where, once beyond, the singularity is always in their finite future. No matter what you do inside, you will reach it at some point. [1]: https://en.wikipedia.org/wiki/Proper_time https://en.wikipedia.org/wiki/Proper_time
    - antognini 3y ago
Paul-Craft 3y ago
I haven't read the paper, but I suspect the whole concept of a 4, 5, 6, or 7-dimensional black hole is nonphysical, but the math works out if you just close your eyes and assume such a thing can exist. The reason I suspect n=7 is as high as it goes is because the volume to surface area ratio of an n-dimensional sphere is r/n, which means that the higher n you have, an n-sphere of radius r has a much larger boundary for the same volume. Conversely, that means that for a given surface area, you have less volume, so, for a constant mass density, you're enclosing less "stuff" inside.
- akomtu 3y ago
  What prevents the formation of many sub-universes with different space-time configurations? We happen to live a large 3+1 one, but others may exist. Speculating further, some black holes could be bridges between e.g. a 3+1 world and a 4+3 world. The observation about 7-dimensional spaces would mean that above that level there are no such boundaries between world, they all become one universe.
  - tsimionescu 3y ago
    I believe that when people talk about N-dimensional spaces they typically talk about spaces with a Euclidean metric unless they explicitly say otherwise. The properties of a sphere in an N-dimensional Euclidean space are not all the same as those in an N-dimensional Minkowski-like spacetime (either 6+1 or 4+3 or any combination).
- codethief 3y ago
  > The reason I suspect n=7 is as high as it goes is because the volume to surface area ratio of an n-dimensional sphere is r/n, which means that the higher n you have, an n-sphere of radius r has a much larger boundary for the same volume. No, I haven't read the paper in detail either, but the reason is very likely the same for why Schoen & Yau (mentioned in the article) could initially only prove their Positive-Mass Theorem up to spatial dimension n=7: In n=8 spatial dimensions minimal hypersurfaces can suddenly develop singularities[0] and you can no longer treat them as manifolds but need tools from geometric measure theory (so-called minimal currents) to describe them. This makes proofs relying on minimal-surface theory in dimensions n > 7 much, much harder (though not necessarily impossible). [0]: The singularities, when zooming in, essentially look like the tip of the 7-dimensional Simons' cone, https://encyclopediaofmath.org/wiki/Simons_cone https://encyclopediaofmath.org/wiki/Simons_cone , making the latter the prototypical example. In fact, the existence of Simons' cone is the whole reason why (i.e. essential to the proof that) stable minimal hypersurfaces in n > 7 can have singularities but in lower dimensions they cannot and are instead smooth: There are no singular stable minimal hypercones in lower dimensions.
codethief 3y ago
> The article says 4+ dimension black holes can exist. Unfortunately, the article is not particularly precise here. The actual statement is that if you're in n < 7 spatial dimensions, then the existence theorem of the paper holds. (I.e. if conditions A, B and C are met, there will be a black hole, more specifically an apparent horizon.) As far as we know, we are in n=3 spatial dimensions, though. (Yes, string theory claims something else but the results of the paper only hold for n non-compactified spatial dimensions, so they don't apply to string theory.)

seeknotfind 3y ago

Came to comment about the same thing. It's funny - higher dimension black holes can confidently exist in a model, but because the model isn't tied to reality, it's not a very meaningful statement. Time ends at black holes. They stretch out time infinitely, from an outside perspective.

SanderNL 3y ago
Time ends at black holes. Is it even possible to empirically validate such a thing?
- BSEdlMMldESB 3y ago
  > Is it even possible to empirically validate such a thing? I wouldn't think so because empiricism implies experience which implies time
- make3 3y ago
  only for outside observers... you can validate it if you go in :)
- bmitc 3y ago
  I think what they meant by end is that time appears to stop at the event horizon for outside observers. As something approaches a black hole event horizon, time appears to infinitely slow, for an outside observer, such that a frozen image of the object gets stuck on the event horizon. But this image can't be seen because it gets infinitely red shifted such that no detection device can keep up with the longer and longer wavelengths.
- GoblinSlayer 3y ago
  You can measure time dilation at different distances from black hole, then extrapolate and see that time dilation goes to infinity at the event horizon.

antognini 3y ago

Black holes already have a time component since they exist in a universe with 3-dimensional space and 1-dimensional time. The equations include both the spatial components and the temporal components. One of the curious features of black holes is that they reverse the roles of time and space in a sense. In ordinary space we have freedom to move around in space, but are constrained to only move forward in time. Different reference frames may move forward at different rates relative to us, but they always move forward. By contrast, once you pass the event horizon of a black hole, these properties swap. It's possible to "move freely" in time in the sense that you can find reference frames that appear to move backwards in time. But all these reference frames are constrained to move forward in space.

Sniffnoy 3y ago
The article explicitly says that it's talking about number of spatial dimensions, it's not including time. It says the new theorem shows that black holes can form into up to 7 spatial dimensions (plus 1 for time). (This isn't to say they can't form beyond that, just this new theorem doesn't show that.)
Zamicol 3y ago
According to GR, time stops at the event horizon. It would take infinite time to cross the event horizon. Everything past the event horizon is speculative.
- magicalhippo 3y ago
  Not really. It just appears to take an infinite amount of time for an outside observer. For someone falling into a black hole, it takes a finite amount of proper time[1] to reach the event horizon. For that infalling observer, the horizon is a boundry where, once beyond, the singularity is always in their finite future. No matter what you do inside, you will reach it at some point. [1]: https://en.wikipedia.org/wiki/Proper_time https://en.wikipedia.org/wiki/Proper_time
  - antognini 3y ago

Paul-Craft 3y ago

I haven't read the paper, but I suspect the whole concept of a 4, 5, 6, or 7-dimensional black hole is nonphysical, but the math works out if you just close your eyes and assume such a thing can exist. The reason I suspect n=7 is as high as it goes is because the volume to surface area ratio of an n-dimensional sphere is r/n, which means that the higher n you have, an n-sphere of radius r has a much larger boundary for the same volume. Conversely, that means that for a given surface area, you have less volume, so, for a constant mass density, you're enclosing less "stuff" inside.

akomtu 3y ago
What prevents the formation of many sub-universes with different space-time configurations? We happen to live a large 3+1 one, but others may exist. Speculating further, some black holes could be bridges between e.g. a 3+1 world and a 4+3 world. The observation about 7-dimensional spaces would mean that above that level there are no such boundaries between world, they all become one universe.
- tsimionescu 3y ago
  I believe that when people talk about N-dimensional spaces they typically talk about spaces with a Euclidean metric unless they explicitly say otherwise. The properties of a sphere in an N-dimensional Euclidean space are not all the same as those in an N-dimensional Minkowski-like spacetime (either 6+1 or 4+3 or any combination).
codethief 3y ago
> The reason I suspect n=7 is as high as it goes is because the volume to surface area ratio of an n-dimensional sphere is r/n, which means that the higher n you have, an n-sphere of radius r has a much larger boundary for the same volume. No, I haven't read the paper in detail either, but the reason is very likely the same for why Schoen & Yau (mentioned in the article) could initially only prove their Positive-Mass Theorem up to spatial dimension n=7: In n=8 spatial dimensions minimal hypersurfaces can suddenly develop singularities[0] and you can no longer treat them as manifolds but need tools from geometric measure theory (so-called minimal currents) to describe them. This makes proofs relying on minimal-surface theory in dimensions n > 7 much, much harder (though not necessarily impossible). [0]: The singularities, when zooming in, essentially look like the tip of the 7-dimensional Simons' cone, https://encyclopediaofmath.org/wiki/Simons_cone https://encyclopediaofmath.org/wiki/Simons_cone , making the latter the prototypical example. In fact, the existence of Simons' cone is the whole reason why (i.e. essential to the proof that) stable minimal hypersurfaces in n > 7 can have singularities but in lower dimensions they cannot and are instead smooth: There are no singular stable minimal hypercones in lower dimensions.

codethief 3y ago

> The article says 4+ dimension black holes can exist. Unfortunately, the article is not particularly precise here. The actual statement is that if you're in n < 7 spatial dimensions, then the existence theorem of the paper holds. (I.e. if conditions A, B and C are met, there will be a black hole, more specifically an apparent horizon.) As far as we know, we are in n=3 spatial dimensions, though. (Yes, string theory claims something else but the results of the paper only hold for n non-compactified spatial dimensions, so they don't apply to string theory.)