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Can someone explain the significance of the connection to five-dimensional black holes / "black strings"? To my layman ears that sounds like a entirely theoreti

Can someone explain the significance of the connection to five-dimensional black holes / "black strings"? To my layman ears that sounds like a entirely theoretical construct that doesn't actually exist. Does/ might it somehow help understanding black holes in our universe better?

cgriswald 7y ago
A problem in the study of what happens when black holes form is that at such insanely small scales the general relativity model of gravity breaks down because of quantum effects. A similar problem occurred in the formation of drops and bubbles where at those tiny scales right before it pinches off molecular effects come in to play. However, through a mathematical method, scientists were able to ignore those molecular effects. Black strings are entirely hypothetical. Scientists are hoping they can be pinched off in the same way as bubbles and that, if they can, they can use the same method above to ignore quantum effects (in the way molecular effects are ignored in bubbles). If so, it could (theoretically) be applied to the study of black holes, allowing scientists to study black holes without a quantum theory of gravity.
BlackFly 7y ago
The fifth dimension is theoretical, yes. It turns out that you can get classical electricity and magnetism out of the Einstein equations by adding a fifth, rotationally symmetric spatial dimension (https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory). Some people had hopes that quantum mechanics could fall out of the einstein equations in a similar fashion and this hope sort of lead to string theory, which needs to add further dimensions beyond the rotationally symmetric U(1) group of Kaluza-Klein theory to support the SO(3) (I believe) group of the electro-weak force (so they add 4 more dimensions) then further dimensions for the strong force symmetries. This latter part isn't my specialty so I am hazy on the details, but it falls under gauge theory. So, while the fifth dimension is at the moment largely theoretical, it holds some interest in the field of gravitational physics due to some elegant constructions that fall out of it. It may be that the scalar field it predicts could describe dark matter: https://arxiv.org/abs/hep-ph/0207125 https://arxiv.org/abs/hep-ph/0207125.
- pdonis 7y ago
  > the SO(3) (I believe) group of the electro-weak force (so they add 4 more dimensions) then further dimensions for the strong force symmetries. The gauge group of the Standard Model, i.e., including electroweak and strong interactions, is SU(3) X SU(2) X U(1) (modulo some technicalities that I don't think matter for this discussion). This is a six-dimensional group, so you need six compactified dimensions in addition to the four dimensions of spacetime that we know in order to construct a Kaluza-Klein/string theory type model that includes all the Standard Model interactions. AFAIK the Calabi-Yau manifolds that are talked about in string theory are examples of six-dimensional compactified spaces that can be used in such a model.
  - BlackFly 7y ago
    That sounds like the details I was hazy on. Thanks.

cgriswald 7y ago

A problem in the study of what happens when black holes form is that at such insanely small scales the general relativity model of gravity breaks down because of quantum effects. A similar problem occurred in the formation of drops and bubbles where at those tiny scales right before it pinches off molecular effects come in to play. However, through a mathematical method, scientists were able to ignore those molecular effects. Black strings are entirely hypothetical. Scientists are hoping they can be pinched off in the same way as bubbles and that, if they can, they can use the same method above to ignore quantum effects (in the way molecular effects are ignored in bubbles). If so, it could (theoretically) be applied to the study of black holes, allowing scientists to study black holes without a quantum theory of gravity.

BlackFly 7y ago

The fifth dimension is theoretical, yes. It turns out that you can get classical electricity and magnetism out of the Einstein equations by adding a fifth, rotationally symmetric spatial dimension (https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory). Some people had hopes that quantum mechanics could fall out of the einstein equations in a similar fashion and this hope sort of lead to string theory, which needs to add further dimensions beyond the rotationally symmetric U(1) group of Kaluza-Klein theory to support the SO(3) (I believe) group of the electro-weak force (so they add 4 more dimensions) then further dimensions for the strong force symmetries. This latter part isn't my specialty so I am hazy on the details, but it falls under gauge theory. So, while the fifth dimension is at the moment largely theoretical, it holds some interest in the field of gravitational physics due to some elegant constructions that fall out of it. It may be that the scalar field it predicts could describe dark matter: https://arxiv.org/abs/hep-ph/0207125 https://arxiv.org/abs/hep-ph/0207125.

pdonis 7y ago
> the SO(3) (I believe) group of the electro-weak force (so they add 4 more dimensions) then further dimensions for the strong force symmetries. The gauge group of the Standard Model, i.e., including electroweak and strong interactions, is SU(3) X SU(2) X U(1) (modulo some technicalities that I don't think matter for this discussion). This is a six-dimensional group, so you need six compactified dimensions in addition to the four dimensions of spacetime that we know in order to construct a Kaluza-Klein/string theory type model that includes all the Standard Model interactions. AFAIK the Calabi-Yau manifolds that are talked about in string theory are examples of six-dimensional compactified spaces that can be used in such a model.
- BlackFly 7y ago
  That sounds like the details I was hazy on. Thanks.