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The "no-hair theorem" says that black holes only have three properties: mass, angular momentum and electric charge. If a black hole is perturbed (for example,

The "no-hair theorem" says that black holes only have three properties: mass, angular momentum and electric charge. If a black hole is perturbed (for example, by merging with another black hole or swallowing a star), it will temporarily be more complicated, but then it quickly goes back to having only above three properties. The extra properties (such as the gravitational quadrupole moment) asymptomatically decay, over a relatively short timespan.

btilly 4y ago
The "no hair theorem" is a theorem of classical general relativity. Attempts to try to model it with some quantum mechanics thrown in show a tremendous amount of additional state that scales with the surface area of the black hole. This work suggests even more complications to that picture. That it looks very different from the classical theory. All of this should come with disclaimers and fudge factors because of our lack of a real theory reconciling GR with QM.
- DiogenesKynikos 4y ago
  Black holes probably have additional state in a full quantum theory, such as lepton number. However, to an extremely good approximation, they'll still look like objects with just three properties.
  - pmayrgundter 4y ago
    In this paper they're talking about spinning black holes, the "Kerr" solutions to GR. Iiuc, there's a lot more structure with these type. See the table on this page for the categories: https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric
  - btilly 4y ago
    Current thinking is that black holes have a LOT of state, not just a little. Anything else would result in loss of entropy. See https://physics.stackexchange.com/a/163046/6796 https://physics.stackexchange.com/a/163046/6796.
    - raattgift 4y ago
      That's only current thinking in SYM/string/D-brane circles, surely? Strominger & Vafa (at the link) is explicitly about N=5 AdS_2 x S^3. Ok, nice that you get unitarity above all in that, but it's not at all clear that the picture corresponds with our universe. I do not see how it could possibly correspond with the universe of the linked article. Croker, Weiner et al. (the authors of the topic paper) are keen first and foremost on their spinning black hole interior solution, which is wholly classical and found at <https://arxiv.org/abs/2107.06643 https://arxiv.org/abs/2107.06643>. In the more recent topic paper they argue that they can make the exterior solution well-behaved too, following the path McVittie paved in 1933 in embedding massive objects in an expanding classical spacetime. They don't come to the end of the path though. As they say in <https://iopscience.iop.org/article/10.3847/2041-8213/acb704 https://iopscience.iop.org/article/10.3847/2041-8213/acb704> §4.6, their desired combination of interior solution, initial formation, infall/merger, arbitrary angular momentum, and being easy to embed in an expanding Robertson-Walker universe is far from complete (There are "known exact solutions with each [property] ... there is no known solution that possesses all [of them]"), they're just hoping to find one. It is not at all clear to me that they have a strong idea about no-hair in their compact objects' causal structure. (I guess totally wildly that it will sensitively depend on the details of the embedding. See Visser 2014 <https://arxiv.org/abs/1407.7295 https://arxiv.org/abs/1407.7295>). Also, it strikes me that their entire idea is to avoid strong gravity in the interior of collapsed stars and in particular avoid the singularity, so one should really think of this as an anti-quantum-gravity approach to black holes, or at least an approach that might evade perturbative non-renormalizability. No extra dimensions, no boundaries, nothing special in the stress-energy tensor, mute on the subject of entropy (which in any case should be thought about in comparison with the huuuuuuuge entropy from the expanding space. Expansion is after all the focus of the topic paper, and so it's rather distant from anti-de Sitter ideas).
      - btilly 4y ago
        This is officially above my paygrade. I just know the basic argument that if black holes are simple, then going from a complex thermodynamic arrangement without a black hole to one with a black hole would represent a spontaneous reduction in entropy. And therefore theories where black holes have a lot of entropy are of interest. While this was originally an argument for string theory, it can be used to argue for other theories as well. I can't opine on your wild guess that how much hair their model of a not-quite black hole is depends on the embedding. But if it is true, I would expect that embeddings that give it a lot of hair are going to be of more interest than the ones that give it no hair exactly for the thermodynamic reason that I gave.

btilly 4y ago

The "no hair theorem" is a theorem of classical general relativity. Attempts to try to model it with some quantum mechanics thrown in show a tremendous amount of additional state that scales with the surface area of the black hole. This work suggests even more complications to that picture. That it looks very different from the classical theory. All of this should come with disclaimers and fudge factors because of our lack of a real theory reconciling GR with QM.

DiogenesKynikos 4y ago
Black holes probably have additional state in a full quantum theory, such as lepton number. However, to an extremely good approximation, they'll still look like objects with just three properties.
- pmayrgundter 4y ago
  In this paper they're talking about spinning black holes, the "Kerr" solutions to GR. Iiuc, there's a lot more structure with these type. See the table on this page for the categories: https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric
- btilly 4y ago
  Current thinking is that black holes have a LOT of state, not just a little. Anything else would result in loss of entropy. See https://physics.stackexchange.com/a/163046/6796 https://physics.stackexchange.com/a/163046/6796.
  - raattgift 4y ago
    That's only current thinking in SYM/string/D-brane circles, surely? Strominger & Vafa (at the link) is explicitly about N=5 AdS_2 x S^3. Ok, nice that you get unitarity above all in that, but it's not at all clear that the picture corresponds with our universe. I do not see how it could possibly correspond with the universe of the linked article. Croker, Weiner et al. (the authors of the topic paper) are keen first and foremost on their spinning black hole interior solution, which is wholly classical and found at <https://arxiv.org/abs/2107.06643 https://arxiv.org/abs/2107.06643>. In the more recent topic paper they argue that they can make the exterior solution well-behaved too, following the path McVittie paved in 1933 in embedding massive objects in an expanding classical spacetime. They don't come to the end of the path though. As they say in <https://iopscience.iop.org/article/10.3847/2041-8213/acb704 https://iopscience.iop.org/article/10.3847/2041-8213/acb704> §4.6, their desired combination of interior solution, initial formation, infall/merger, arbitrary angular momentum, and being easy to embed in an expanding Robertson-Walker universe is far from complete (There are "known exact solutions with each [property] ... there is no known solution that possesses all [of them]"), they're just hoping to find one. It is not at all clear to me that they have a strong idea about no-hair in their compact objects' causal structure. (I guess totally wildly that it will sensitively depend on the details of the embedding. See Visser 2014 <https://arxiv.org/abs/1407.7295 https://arxiv.org/abs/1407.7295>). Also, it strikes me that their entire idea is to avoid strong gravity in the interior of collapsed stars and in particular avoid the singularity, so one should really think of this as an anti-quantum-gravity approach to black holes, or at least an approach that might evade perturbative non-renormalizability. No extra dimensions, no boundaries, nothing special in the stress-energy tensor, mute on the subject of entropy (which in any case should be thought about in comparison with the huuuuuuuge entropy from the expanding space. Expansion is after all the focus of the topic paper, and so it's rather distant from anti-de Sitter ideas).
    - btilly 4y ago
      This is officially above my paygrade. I just know the basic argument that if black holes are simple, then going from a complex thermodynamic arrangement without a black hole to one with a black hole would represent a spontaneous reduction in entropy. And therefore theories where black holes have a lot of entropy are of interest. While this was originally an argument for string theory, it can be used to argue for other theories as well. I can't opine on your wild guess that how much hair their model of a not-quite black hole is depends on the embedding. But if it is true, I would expect that embeddings that give it a lot of hair are going to be of more interest than the ones that give it no hair exactly for the thermodynamic reason that I gave.