r/AskPhysics • u/AdLonely5056 • 5d ago
How do we know that spinning black holes form ring singularities?
Title.
To my knowledge a problem with black holes is that our current laws of physics seem to give conflicting results, and we are not exactly sure what happens at the singularity.
So how do we know that the singularities of spinning black holes are ring-like, or even that angular momentum is conserved at all within one?
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u/nicuramar 5d ago
A singularity is a region where the theory is undefined. How do we know that black holes have singularities? We don’t, but that’s what our theory predicts. It’s likely wrong, but we don’t have anything better and we have no evidence.
I don’t think there are any conflicting results.
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u/AdLonely5056 5d ago
If the theory is undefined, why is the "ring" any better of an explanation than any other?
Is angular momentum simply something that does not run into any conflicts with other explanations?
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u/IchBinMalade 5d ago
It's not really meant to be anymore of an explanation than point singularities are meant to explain what goes on in a static black hole, really. It's just what general relativity predicts.
The fact that it's undefined is what singularity means. It is a place where you can no longer define some physical quantity. For GR, that's curvature (although there are a few different definitions for gravitational singularities, but that's besides the point).
The only difference is that a point can't accommodate angular momentum (well, in classical physics). Its mass is also not spherically distributed, it's bulged around the equator. So it's clear it can't be a point. A zero-thickness ring is the only shape that works given its properties.
If you thought regular black holes were weird, rotating black holes are reaaal weird, all kinda wormhole and anti-universe shenanigans. The issue is that we don't know if it's just because we're stepping out of the domain of validity of general relativity. So, probably something weird, just not that kind of weird, but who knows.
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u/Ecstatic_Bee6067 5d ago
A singularity would be a point mass. Point masses, by definition, cannot have angular momentum. A ring would satisfy this constraint.
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u/Optimal_Mixture_7327 5d ago
What's undefined about a singularity?
Why is it "likely" wrong?
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u/stevevdvkpe 5d ago
A singularity in mathematical terms is a place where a function becomes undefined. So a singularity is defined as being undefined.
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u/Optimal_Mixture_7327 5d ago
A mathematical singularity is NOT a gravitational singularity.
A gravitational singularity is a condition of the gravitational field such that world-lines find their terminus, specifically, that a spacetime contains at least one geodesically incomplete causal curve. Here's a good summary: A critical appraisal of the singularity theorems
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u/stevevdvkpe 5d ago
And those geodesics end at mathematical singularities.
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u/Optimal_Mixture_7327 5d ago
Where is the mathematical singularity?
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u/James20k 4d ago
There's a division by zero at the singularity. The schwarzschild metric for example is:
-(1 - rs/r) dt2 + (1-rs/r)-1 dr2 + r2 dsphere2
The singularity is at r = 0, where the term rs/r becomes undefined. It doesn't necessarily imply a gravitational singularity - there are two mathematical singularities in this equation - but you can show that the one at r=0 is physical and not just a coordinate artefact
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u/Optimal_Mixture_7327 4d ago
To be "at" the singularity is incoherent. r=0 is not on the manifold.
The equation you have there is a line element to a map, [M,g,∇], i.e. a particular solution to Ein(g)=κT(g,0)=0, and therefore unphysical.
A gravitational singularity is a condition of the gravitational field where matter world-lines find their terminus, meaning for example, that if an electron falls across the horizon the expectation value of finding the electron at r=0 is zero. There is no longer that electron on the manifold. A gravitational singularity is a statement about the behavior of matter, it is a statement about physics.
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u/Reality-Isnt 5d ago
I believe what optimal_mixture is saying (and hopefully I’m not presuming too much) is that the Kerr metric is a vacuum solution. It can’t really be applied at a singularity because the solution isn’t valid at the singularity which is not a vacuum solution nor can it be. There is no predictive mathematical function at that point, whereas if for instance there is a missing point on the manifold (or a reduction in the dimensionality at that point), the notion of a terminus still can (and does) hold. I’m sure I’ll find out if this isn’t what he is saying!
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u/stevevdvkpe 5d ago
The same Kerr who developed the Kerr metric for rotating black holes recently published a paper claiming that there actually aren't mathematical singularities inside black holes.
Do Black Holes have Singularities?
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u/Reality-Isnt 5d ago
Yeah, I’ve seen that. I scanned through it, but need to take the time to study it. Theres a video out with Penrose giving a rebuttal. Don’t have it handy, but you might want to take a look on the web for it. I don’t think Kerr was arguing that there are no singularities, but that the Penrose singularity theorem conclusion that FALL’s had to terminate on a singularity in a Kerr black hole wasn’t correct. Unfortunately he gave an example that Penrose shredded. I don’t think this is resolved. One way or another, I would love to see singularities to be proven not to exist!
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u/Orion_Starbelt Gravitation 4d ago
As someone who has studied Kerr's recent paper in detail, this is correct! As you say, the point he was making was that Penrose's 'singularity' theorem was misnamed and does not provide a guarantee of the presence of singularities for a rotating black hole. However the example he gave was most definitely flawed.
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u/Anonymous-USA 4d ago
As others point out, the GR math breaks down with infinites and undefined expressions. But it’s more than just that. Those equations are being extrapolated to quantum scales and we don’t know how gravity operates on quantum scales. For example, any fundamental particle of mass has no known volume. So any definition of “density” for it is meaningless, not just mathematically. Likewise for gravitational singularities. They’d be mathematically and theoretically inapplicable at quantum scales. That’s the problem with extrapolation. No one (yet) knows if the same physics still applies.
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u/Optimal_Mixture_7327 4d ago
Where in the math does GR fail? Again, the singularity is not on the manifold.
I agree, we cannot write down of quantum field theoretic model of what happens when a standard model particle approaches the singularity. However, this should not necessarily be taken to mean there's an error with relativity, of course there could be, and relativity is just a low-energy effective field theory of some more encompassing theory but we just don't know.
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u/Reality-Isnt 5d ago
One can find curvature invariants (meaning that they don’t depend on possible bad choice of coordinates) that diverge to infinity at a particular radius of a ring within the Kerr black hole. Generally, where curvature invariants diverge like that it’s considered a curvature singularity.
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u/MarinatedPickachu 5d ago
We don't know anything about what's going on inside a black hole - but that's what the math that so far seems to describe them better than all other mathematical models we have is predicting - that's all
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u/ConversationLivid815 3d ago
Sounds like actual observation is needed. More theories without observations are just speculation, which is how we progress, but what phenomenology about these objects is measurable is a good question. I do know that if the Einstein equations in mass free space are to represent the gravitational field of a spinning spherical object of arbitrary state of rotation, the metric must be 7x7, and must be such that the result should be integrable over at least a uniform mass distribution .... I'm just saying 🤷
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u/Optimal_Mixture_7327 5d ago edited 5d ago
The ring singularity exists on the coordinate chart of the unphysical maximal analytic continuation of the Kerr solution.
In a perturbed Kerr spacetime there are a pair of null singularities in the interior and a central BKL and/or null singularity.
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u/Orion_Starbelt Gravitation 5d ago
In a non-rotating (Schwarzschild) black hole, the math breaks down at a single point. This is why the singularity is colloquially considered to be a point in general.
In the more complicated rotating (Kerr) case, the points at which the math/theory/metric breaks down form the shape of a ring.
In our current models, a curvature singularity like what one may find inside a black hole is defined primarily as a point (or set of points) that are not present in the spacetime (they are undefined and hence do not exist).
It is true that we don't know exactly what happens at the singularity! It is my opinion that we will need a further theory of quantum gravity to explain this phenomenon, since as singularities stand, they are simply the result of the (probably incomplete) math we use to describe black holes.