Does a black hole have to have a point-like singularity at its core?

It seems to me that everything I read about black holes mentions that at the centre there is an infinitely dense one-dimensional point called a singularity.

As far as my basic understanding goes - when a suitable massive star reaches its end of life, gravity forces all its electrons, protons and neutrons to fuse together causing a neutron star. If the star was too massive to begin with these neutrons will then be forced together by gravity into a infinite density causing a singularity and a black hole.

What would happen if there was something type of matter that was denser than neutrons so that a star could form that had an escape velocity greater than the speed of light. Could we not have a black hole that had a solid surface somewhere inside the event horizon?

Is there any reason that such a dense form of matter could not theoretically exist? Is it because of the speed of light/space-time curvature/something else that anything inside the event horizon must end up in a singularity.

A possible alternative way of looking would be - what if the speed of light was only 10km/s wouldn’t the earth be a black hole but with a solid surface inside the event horizon?

Thanks

There are postulated forms of matter even denser than neutron stars, resulting in even smaller objects called quark stars.

But for there to be anything non-point inside of a black hole would defy all that we know of physics. Simply put, matter fundamentally cannot be that strong. It’s beyond even being a matter of strength: We’re into comic-book-Superboy-changing-reality-by-punching-the-fabric-of-space territory, here.

Which is not to say that our understanding of physics can’t be wrong. Most attempts at a theory of quantum gravity predict that there’s something of very small (but nonzero) size in there. But we can’t yet get any theory of quantum gravity to work, so that’s all just speculation.

I’m not disagreeing with you when you say that matter cannot be that strong but my (simplistic) train of thought is that if there was something theoretically twice as strong/hard as neutrons then this star would be twice(?) as small as a neutron star. If we then had something twice as strong/hard as this new material then that star would be smaller and so on. It would then seem that at some stage something would be hard enough to form a star where the escape velocity is greater than c and then we have my black hole with a surface.

Where is my thinking incorrect? Is it the fact that the escape velocity is greater than c that means this matter cannot exist and if so, does that it would be theoretically possible we could have a sphere where the escape velocity is 0.99999999c just not one where it is c?

Just thinking a bit about this - is this because the entire volume of the star inside the black hole is going to end up in the singularity because of the switching of space and time inside a black hole?
The same way the singularity is in the future inside a black hole just as Tuesday is in my future and also just as inevitable?

Yup, that’s it exactly.

To your other question, there’s no fundamental reason why you couldn’t have a substance or object that’s just barely shy of becoming a black hole-- In fact there has been some serious scientific speculation about just such objects, usually called “gravatars”. Most mainstream physicists consider the idea absurd, because it just requires far too much fine-tuning and hand-waving, but it’s not completely in the realm of crackpottery.

Also, there’s a significant number of physicists who think that a black hole doesn’t actually collapse to a singularity, that a quantum theory of gravity will show that some other effect intervenes. The problem is that we don’t have a working quantum theory of gravity yet, so this is pretty much just speculation. For example Loop Quantum Gravity, one proposed theory, predicts that a star would start to collapse to a black hole, then quantum gravity effects would cause it to stop and bounce back, but because of time dilation the bounce would take too long for us to observe directly. Quantum bounce could make black holes explode | Nature

I must say that a lot of things to do with black holes and relativity seem very weird/counter-intuitive to me but that’s obviously my problem. The one thing that really seems impossible to me is how can the singularity be infinitely dense? It just seems “obvious” (:)) to me that would have to be a certain finite density. Loop quantum gravity mentioned in the article by Pantastic seems like at least a nice alternative

Still very interesting to think about and try to understand even if I realize my understanding of these topics is only skin deep/

Thanks for the answers.

Density is a function of mass and volume - if the object has zero dimensions, and any mass, the density has to be… well… incalculable - it’s a divide-by-zero problem, I think.

What’s less intuitive to me personally is how two of them can have different masses when their density is infinite and their size is the same - but I guess that’s probably because ‘infinite’ itself isn’t an intuitive concept, and ‘the same’ probably doesn’t apply here.

It’s exactly a divide-by-zero problem. That’s why it’s called a singularity, after all: In mathematics, a singularity is a point where a function is either undefined or “blows up” or becomes ill-behaved in some way. As a trivial example, 1/x is singular for x = 0.

So a singularity in a black hole is a point where our functions to describe reality blow up: Finite mass in zero volume is a divide-by-zero moment. In a deep sense, the fact we have a singularity is more of a reflection of our ignorance than any physical reality, because the physical world makes sense. The physical world doesn’t have any nonsensical parts, just parts we haven’t learned how to make sense of yet.

This, actually, makes perfect sense: Fundamental conservation laws must hold, so as long as the black hole didn’t emit a huge burst of energy or get a massive influx of matter or something, it has to have approximately the same mass as the collapsing degenerate matter which formed it. Anything else would do truly nasty things to the logical consistency of our theories.

How in the world would infinite curvature and a singularity actually look in 4D space? The singularity would be at what time? Time = infinite?

How does that reconcile with the fact that black holes seem to radiate? If a black hole radiates x amount of mass-energy at t = y wouldn’t that imply that the mass distribution would reflect that?

At the instant right before y the black hole is mass M+x and at the instant y the black hole is now mass M how can the components of the black hole be chilling at the singularity?

Plus how can you argue with Stephen Hawking? Stephen Hawking: 'There are no black holes' | Nature

Sure - the counterintuitive part is how a massive singularity and a less massive singularity can have different masses, but be the same size, and both be infinite density - i.e. ‘the same’ density (I know there are different sizes of infinity, but I don’t think these are those, although this could well be a Hilbert case of infinity+1 still being infinite, and the same size of infinite), but it goes back to the collapse of function - they’re only ‘the same’ because the result of any divide-by-zero is ‘the same’.

That depends on what reference frame you’re measuring time in. To anyone inside of a black hole, the singularity is the future, and arrives after all too short a time.

The usual way of representing black holes in 3+1 dimensions is via Penrose diagrams.

Maybe someone could explain this to me. From the POV of an observer falling into a black hole, because of time dilation, the rest of the universe around you would speed up so much that the entirety of the universe’s life would play out while you’re still falling. Doesn’t that mean that from our POV outside the black hole, that the things falling in never finish falling in?

I’ve always favored the idea that there will be no relativistic singularity but will be some weird quantum state. Sure, it’s speculation, but so is the explanation of the singularity!

Yes, but the point is moot, because you’ll very quickly receive the last photon from the poor sod falling in.

Penrose proved that, in general relativity with the assumption of non-negative mass density, there is always a singularity where there is a black hole. However there is nothing to say that a singularity must be “point-like” or “ring-like” (as in the case of a Kerr black hole) or any designation that suggests it is somewhat similar to a spatial location/shape.

This is not true. If you take Schwarzschild example: for a given observer crossing the event horizon at a certain time there’s a very definite and finite limit as to how far in the future of the black hole exterior they will be able to see before they hit the singualrity.

Actually that’s not strictly true as if, once they hit the event horizon, the observer travels arbitrarily close to the speed of light radially outwards from the black hole they can observe arbitrarily far in the future. However at the moment an observer hits the singularity they will not be witnessing the infinite future of the exterior.

What the poster is struggling with, as am I, is some kind of intuitive explanation for the apparent paradox between the “frozen in time” consequence of infinite time dilation and the fact that according to everything we know both empirically and theoretically, matter does fall into black holes in a pretty straightforward Newtonian fashion, creating powerful accretion disks in the process, and black holes become more massive accordingly.

My attempts to gain an intuitive non-mathematical insight into this apparent paradox may or may not be sound, so I invite appropriate criticism. They have centered around the idea that this apparent freezing due to infinite time dilation is merely an artifact that arises from the use of inappropriate coordinates and implicit but incorrect assumptions about simultaneity. The Schwarzschild solution to the Einstein field equations for a non-rotating black hole (and the equivalent Kerr solution for a rotating one) are valid as one approaches the event horizon and can be used to show the aforementioned switching of the time dimension with the radial spatial dimension beyond the EH, but it’s ill-behaved at the EH itself, where it blows up and appears to show the time dilation factor tending to infinity as the distance to the EH tends to zero. However under the appropriate geometries and coordinate systems the spacetime curvature at the EH can be shown to be well-behaved and finite.

There seem to be multiple different ways of trying to grasp this intuitively. One way is that from the perspective of an external observer, time dilation really does freeze the infalling object – in space. But the Schwarzchild coordinate system that leads to this conclusion also leads to the conclusion that space itself is rapidly flowing into the black hole, exceeding the speed of light beyond the EH (which space is allowed to do, as distinct from objects in it), where time and the spatial dimension pointing to the singularity have correspondingly switched places and the singularity becomes the object’s future.

At no point would you actually see the intrepid astronaut frozen forever at the EH (he’d be red-shifted out of detectability anyway), but more importantly, I’m suggesting that the idea that the astronaut would forever be at rest at the EH as seen by an external observer seems to stem from a misapplication of the Schwarzchild solution.

Yes, exactly. In fact from outside the hole, we never even see the hole actually form in the first place, because the collapsing matter seems slow down and never reach the event horizon. That’s why the Russian name for “black hole” translates as “frozen star”. (Also because “black hole” is a moderately obscene phrase in Russian.)

But as Chronos says, this is theoretical. As a practical matter, the light from the infalling matter dims to invisibility in a finite amount of time.

–Mark

And yet obviously black holes form, since we see evidence of lots of them around, just like we have lots of indirect evidence and theoretical descriptions of matter falling into them, in perfect conformance with Newtonian physics. A star that remains much above the Chandrasekhar limit (and, more specifically, above the Landau-Oppenheimer-Volkoff limit for one that has collapsed into a neutron star) will collapse into a black hole. Few would argue otherwise.

I would argue with your premise, however. As I tried to suggest above, despite the Russian name and the illusion of slowdown to a complete halt of an infalling object, the “freezing” really is an illusion. What we see as the wavelength gets increasingly red-shifted and the photon arrival increasingly longer does not reflect what is happening locally.