Good News on the Black Hole Front

[Gord_in_Toronto]

If anyone has been following along since Stephen Hawking died.

Black Holes Finally Proven Mathematically Stable

There is still much work left to be done as:

So far, stability has only been proved for slowly rotating black holes — where the ratio of the black hole’s angular momentum to its mass is much less than 1. It has not yet been demonstrated that rapidly rotating black holes are also stable. In addition, the researchers did not determine precisely how small the ratio of angular momentum to mass has to be in order to ensure stability.

If some one would care to produce a 200 page summary, it may help my lay comprehension as:

In a 912-page paper posted online on May 30, Szeftel, Elena Giorgi of Columbia University and Sergiu Klainerman of Princeton University have proved that slowly rotating Kerr black holes are indeed stable. The work is the product of a multiyear effort. The entire proof — consisting of the new work, an 800-page paper by Klainerman and Szeftel from 2021, plus three background papers that established various mathematical tools — totals roughly 2,100 pages in all.

 

[Puppycow]

Uhhh, good luck with that.


What I do know is very basic: when the radius of a spinning object gets smaller, it spins faster. The famous example is a figure skater pulling her/his arms in when performing a spin on the ice. A Neutron star is known which spins at 43,000 rpm.

I wonder what their upper limit is for "slowly rotating"? They say "where the ratio of the black hole’s angular momentum to its mass is much less than 1". I wonder what that means in terms of rpm?

 

[Ziggurat]

I wonder what their upper limit is for "slowly rotating"? They say "where the ratio of the black hole’s angular momentum to its mass is much less than 1". I wonder what that means in terms of rpm?

What does rpm's even mean for a black hole? The event horizon is featureless, so it doesn't spin in that sense, and you can't really assign an rpm to the singularity either. It's more like an electron in that sense.

What you could do is measure the rpm's of an object of the same mass and angular momentum just before collapse into a black hole. That's still going to vary depending on mass, I think. Your neutron star example may be in the ball park for stellar mass black holes.

 

[Puppycow]

Well black holes do seem to have a spin nevertheless. They give off great jets of energy from the poles when feeding. I don't really understand why, but we can see it. We cannot see how fast the singularity itself is spinning, but it almost certainly is spinning. I say rpms, because that's the unit I know, but perhaps it doesn't apply. Since the rate of rotation increases as the radius gets smaller, and a black hole singularity has a smaller radius than a neutron star, I imagine it would spin even faster.

 

[RecoveringYuppy]

RPMs aren't a sufficient unit because two things with vastly different mass can be spinning at the same rate and would have very different angular momentum which is the relevant conserved quantity here.

The math you have described verbally will lead to the RPMs being infinite. Not a meaningful answer.

 

[Puppycow]

The math you have described verbally will lead to the RPMs being infinite. Not a meaningful answer.

A very large number, I'm sure. I doubt infinitely large. Isn't it true that as the radius gets smaller, the rate of rotation increases? Also, wouldn't you agree that what I described verbally is actually true?

I'm skeptical that a singularity has an infinitely small radius. Must be at least a Planck length.

 

[HansMustermann]

Well black holes do seem to have a spin nevertheless. They give off great jets of energy from the poles when feeding. I don't really understand why, but we can see it. We cannot see how fast the singularity itself is spinning, but it almost certainly is spinning. I say rpms, because that's the unit I know, but perhaps it doesn't apply. Since the rate of rotation increases as the radius gets smaller, and a black hole singularity has a smaller radius than a neutron star, I imagine it would spin even faster.

All that is somewhat inexact.

For a start, a singularity has a size of zero. It's a point. That's why it's a singularity, really. It doesn't even make sense to say it rotates per se, and momentum conservation would pretty much mean infinite angular speed as you shrink it to zero. That is most certainly not the rotation speed of any known black hole.

Second, as even that page will tell you, it's not the singularity rotation itself that produces those jets. Nothing can escape from inside a black hole, which is where that singularity is. Not even light can get out, much less some ionized matter going at sublight speeds. That matter comes from the accretion disk BEFORE it entered the black hole, and pretty much currently we're not sure how much of it is due to magnetic fields and how much because of frame dragging outside the event horizon.

 

[W.D.Clinger]

I wonder what their upper limit is for "slowly rotating"? They say "where the ratio of the black hole’s angular momentum to its mass is much less than 1". I wonder what that means in terms of rpm?

The Kerr pseudo-metric for a spinning black hole involves a parameter a, which is defined as the intrinsic angular momentum per unit mass.

From Misner, Thorne, and Wheeler §33.2:

For collapse with small charge and small asymmetries, perturbation-theory calculations (Box 32.2) predict a final black hole with external field determined entirely by the mass M, charge Q, and intrinsic angular momentum S of the collapsing star. For fully relativistic collapse, with large asymmetries and possibly a large charge, the final black hole (if one forms) is also characterized uniquely by M, Q, and S. This is the conclusion that strongly suggests itself in 1972 from a set of powerful theorems described in Box 33.1.

For a start, a singularity has a size of zero. It's a point. That's why it's a singularity, really.

The singularity is not a point, but rather the absence of a point. Its absence cannot be repaired by adding a point, because that repair is mathematically impossible: the manifold cannot be extended to remove the singularity.

The singularity tells us the general theory of relativity is inadequate to describe physics in the near vicinity of the singularity. It's a wonderful thing when the theory itself tells you the theory can't be the whole story.

 

[HansMustermann]

Well, ok, it's the point where the maths doesn't work. It's still size zero, that's what I was trying to say.

 

[Puppycow]

All that is somewhat inexact.

For a start, a singularity has a size of zero. It's a point.

In theory, but is there any actual evidence to support that? I thought that "theories break down" when you are talking about a black hole. I believed that most of my life, but I think it's an act of faith. Physics is still a work in progress. And I'm not trying to trash it, either. I find it really amazing how much they've figured out. But, we still don't know everything. Maybe some as-yet-unknown force or law comes into play which keeps it at a finite size greater than zero. I mean, doesn't that strike you as at least slightly dubious, that it is a point of zero size?

 

[HansMustermann]

As W.D.Clinger said, albeit in different words, it's the point where the theory doesn't work. It's where basically you'd divide by zero. Quite literally, since you're dividing by r² (distance from the centre) and you have a problem for r=0. The same doesn't happen if you divide by 1mm or 1nm or even 1 Planck length or whatever. It's only exactly zero that produces that effect. Hence yes, it's a point. It's zero size. Anywhere around it, no matter how close, is NOT part of the singularity.

Ergo talking about the singularity as if it's something bigger, that you could measure the rotation of and whatnot makes no sense. Making it bigger is not the way to fix that.

 

[RecoveringYuppy]

A very large number, I'm sure. I doubt infinitely large.

Yes, infinitely large as others have said now. Because you said singularity.

Isn't it true that as the radius gets smaller, the rate of rotation increases?

Yes, and you described going to zero radius.

Also, wouldn't you agree that what I described verbally is actually true?

I'll just go back and address each point.

I'm skeptical that a singularity has an infinitely small radius.

OK. Pick whatever number you like to imagine and do the arithmetic. You can get any number from whatever starting point you assume up to infinity with that approach.

Must be at least a Planck length.

OK. Why? Do you have a misconception that the Planck is the smallest something can be or that space consists of Planck length cells of some sort?

Well black holes do seem to have a spin nevertheless. They give off great jets of energy from the poles when feeding. I don't really understand why, but we can see it.

I know the article says "spin" in a lot of places but for black holes there is no way to assess spin. It just has angular momentum. We also don't know what the relation of the angular momentum is to the jet. Also don't know if the angular momentum of or powering the jet (if any) is coming from the central object or it's accretion disk. The role of the angular momentum (if any) in forming the jet isn't well known. It may be required for forming a magnetic field but not for "power". A lot of unknowns here.

"spin" is likely to be a confusing word in this context because it is a common word that seems to mean an obvious thing to the average person. When you get down to singularities it is simply no longer obvious. Physicists leave it out (based on the common definition) due to Occam's razor for singularities. It contributes no value. They still use the word "spin" though. But there is no "spinning" in their definition of spin. It's angular momentum. They just assume it's intrinsic angular momentum and don't try to decompose it like you can for macroscopic objects with orbital angular momentum. "Orbital" is also a word that may not mean to a physicist all the thing that it might mean to someone else.

We cannot see how fast the singularity itself is spinning, but it almost certainly is spinning.

There is no certainly at all about that. The couple of misconceptions you have seem to lead to you being certain, but the certain part is angular momentum not "spinning".

I say rpms, because that's the unit I know, but perhaps it doesn't apply.

Explain how it could apply. And I mean with currently known facts.

Since the rate of rotation increases as the radius gets smaller, and a black hole singularity has a smaller radius than a neutron star, I imagine it would spin even faster.

I just recalled that I've heard you advance imaginary evidence before. You should stop and think about what you are saying when you apparently actually realize you are using imaginary evidence. Why don't those words trigger a rethink when you say them?

 

[RecoveringYuppy]

In theory, but is there any actual evidence to support that?

It's a mathematical definition. It's nothing but theoretical. And, in fact, singularities don't have any single agreed upon physical interpretation. If any has a meaning it's meaning has to be derived from other factors.

I thought that "theories break down" when you are talking about a black hole. I believed that most of my life, but I think it's an act of faith.

Forget it then. Faith is not a good way to arrive at truth or even accuracy. And there are actually good reasons to know a theory has broken down and it's not simply because "it's a black hole".

One reason is a singularity showing up in an equation. Another reason is two or more theories leading to conflicting results.

Maybe some as-yet-unknown force or law comes into play which keeps it at a finite size greater than zero.

Well fine, of course. But read your posts. You're not treating this as an unknown. You're insisting there is an answer now.

I mean, doesn't that strike you as at least slightly dubious, that it is a point of zero size?

It simply being zero is not a particular good reason to be dubious.

 

[theprestige]

If anyone has been following along since Stephen Hawking died.

Black Holes Finally Proven Mathematically Stable

There is still much work left to be done as:


If some one would care to produce a 200 page summary, it may help my lay comprehension as:


: boggled :

Sounds like he had to first create a lot of the mathematical tooling he'd need to attempt the proof, and that most of the pages are him proving that the tooling itself is mathematically sound. And the big 800-page paper is probably him assembling the tooling into one big mathematically-rigorous proof assembly line, and then stepping the proof down the line in front of god and everybody.

I bet if other people find the tooling valid and useful, mathematicians will soon come up with basic symbols to summarize a lot of it.

 

[HansMustermann]

@Puppycow
I'll also reiterate the idea that nothing, no information actually escapes a black hole. What the rest of the universe "observes" is all the matter that ever fell into it, plastered around the event horizon, as it were. Hence it's actually irrelevant to focus on the singularity.

The reason we are talking about a singularity at all is that basically we know of no force that would stop the matter from keeping falling at that point. We know that for example neutron stars are partially supported by nuclear forces and partially by neutron degeneracy, but once it's too heavy for those to support, we don't actually know what would keep that matter from just keeping falling all the way to the centre.

But since that would be on the inside of an event horizon, while we're on the other side, we don't really know wth happens there. Is there some other force that kicks in at some point to stop further collapse? Maybe. But that information can't reach us.

But roll that around in your head for a moment: no information from there can reach us.

So focusing on that side to explain stuff outside is rather pointless. If any information about the singularity could reach the matter outside, we would (or at least could) have some evidence there, innit?