Question How does General Relativity predict zero volume/infinite density of Black holes?

[Catastrophe]

Quantum leaps.
IMO they are a means of travel for both gravity and light.
All depends of interaction or non interaction as to what laws apply.
Going form possible info location for light to info location is C speed.
Traveling between info point as gravity/spooky action does takes no time since it travels in no/space/time.

JMO though but answers a fundamental question about gravity instant info exchange and spooky action.

Sorry, but was that a 'yes' or a 'no'?

 

[voidpotentialenergy]

Sorry, but was that a 'yes' or a 'no'?

The minimal jump of a quantum leap is the orbit distance from a hydrogen atom to a helium atom.
IMO that is the distance light must travel in wave/particle format and the minimum chunk of space that exists.
That orbit distance in the quantum world and fact that an orbit never looses or gains energy and you can never be part of an orbit says lots about what is between orbits.
Time just the distance the wave/particle travels C to go from minimum quantum energy level to the next minimum quantum energy level.

Relativity IMO forgets that the universe is made of these chunks and when you compress them so does time/space get compressed.
Why we don't see infinite mass point in a black hole is simply a compression that increases and increases time for more compression.
Never ending compression loop that would take forever to reach an infinite mass point.

 

[IG2007]

So how does General Relativity predict zero volume, when the volume predicted should be incredibly small, but clearly not zero?

That's exactly the point I have been trying to make for while. You cannot compress something to point zero! That would make it unreal and it would take an infinite (aka impossible) amount of time to reach point zero, just like it is impossible to reach Absolute zero.

IMO, at max, a compression can reach only to Planck length and not more than that. Or, maybe not, as, some studies say, that at the time of the big bang, one metre today was much less than the Planck length. You can get that article somewhere around in Space.com. So, who knows if Relativity is correct in assuming that space can be divided into infinite pieces and thus it is impossible to know the least amount of space that can exist? But, I agree that the it is impossible to reach point zero space.

 

[Catastrophe]

We are always going to get into trouble when we continue to scatter around terms and phrases like "absolute", "infinity", and "division by zero". As dear old Korzybski said, "The map is not the territory". Just because a word exists, it does not follow that it reflects an underlying reality. Remember the word "cloudcuckooland"?
We would not, I hope, argue that because pink elephants are alleged to exist in Cloudcuckooland, that they must have existed on Earth, and are therefore extinct. So why do we talk about "division by infinity"? - a process just as ridiculous - except, of course, as part of one of our wonderful mathematical abstractions. "Part of" - of course, not. It is nothing but a mathematical abstraction. Since there is no such real number as infinity (hence we get more rubbish like the 'infinity plus one' arguments) just think of, say, a 50 digit prime number. Now, using long division, divide that into one. Bet you wish you hadn't started!

Density = mass / volume. If it has mass, especially large mass, it will have a real volume, so dividing by that will not give us infinite density. Repeat the above exercise, except divide your 50 digit prime number by a very small number with no common factors, and beginning with 27 noughts. When you have completed both exercises (or given up) you will understand why mathematics was blessed with unreal quantities such as infinity - both infinitely large and infinitely small. Are there any cases in experimental science when you are likely to need the number 0.000000000000000000000000000000000000000000000000000735962715377391362543227772854321? Even the number following the zeros is likely to be way beyond the accuracy limitations of any experiment.

So "How does General Relativity predict zero volume/infinite density of Black holes?".
Well, if it does, it shouldn't. What it really means is very, very high. Or, if you want to be more precise, say "probably greater than 1 x 1 0^77". Inventing words like infinity is just a lazy way of describing seemingly boundless quantities.

Cat

 

[Lariliss]

The no-hair theorem states that all black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.

This metaphor means that during black hole formation the data of the collapsing source is lost [under event horizon].

A black hole is one of the rare cases when the theory was elaborated within math long before any evidence gained. In this ‘singularity’ situation physics laws and their prediction ability are lost.

Limits are a concept from calculus. Mathematically it is useful. But a black hole is a physical system with a very small volume, and a very high density. Although we can imagine the infinite in space and time, no physical system can go there. Singularity - is a missing point of space-time.

 

[Catastrophe]

How does General Relativity predict zero volume/infinite density of Black holes?

Just postulating zero volume and, therefore, infinite density is, in my opinion, a step too far. I am not happy with the 'backward extrapolation' - are the factors including inflation known sufficiently well to extrapolate backwards, or is a straight line (on log paper?) drawn through a splash of points? I cannot accept the idea even of a singularity.

Cat

 

[Lariliss]

to extrapolate backwards, or is a straight line (on log paper?) drawn through a splash of points?

Agree, exactly to the point. That works in math with numbers (also not always).
As we cannot look inside (yet?) physics tug to less literally perceived definitions.
More detailed observation feeding analysis, simulations and concepts.

Here some results: https://phys.org/news/2021-07-magnetic-balding-black-holes-relativity.html

A bit off the subject, but similar confusions come to mass definitions.

 

[Catastrophe]

I am going to go get it, as I am sure I have many versions of plots of the expanding Universe on a graph with x's all over the place - and I don't mean just the local group where we have galaxies coming together against the trend, (Local gravitational attraction overcoming expanding forces),

Here is one: how is that for uniform expansion?

https://imgur.com/a/y9qcNIN

View: https://imgur.com/a/y9qcNIN

and from: Edwin Hubble & the Expanding Universe (csiro.au)

https://imgur.com/a/0qYLORO

View: https://imgur.com/a/0qYLORO


Cat

 

[Catastrophe]

Here is another question for you.

Who says the line on the graph has to go through the origin? This is the only reason that there is zero volume (and infinite density) at 0, 0 (origin). This was an assumption. What if there were lots of good points that gave a line which did not go through the origin? And these points indicated a finite volume at t = 0? That would be a good argument for a cyclic system.

Cat

 

[Lariliss]

Here is another question for you.

Who says the line on the graph has to go through the origin? This is the only reason that there is zero volume (and infinite density) at 0, 0 (origin). This was an assumption. What if there were lots of good points that gave a line which did not go through the origin? And these points indicated a finite volume at t = 0? That would be a good argument for a cyclic system.

Cat

With the same interest, I am on it.
Thank you for the good formulation.
Starting. There is always question to keep in mind for me, that if there is no clear prove, shouldn't it be to put to trial to 'disprove' (general formulation).

 

[Catastrophe]

That should be the way. Offer models to be shot down, providing the models have some intrinsic substance.

Cat

 

[voidpotentialenergy]

How does General Relativity predict zero volume/infinite density of Black holes?

Just postulating zero volume and, therefore, infinite density is, in my opinion, a step too far. I am not happy with the 'backward extrapolation' - are the factors including inflation known sufficiently well to extrapolate backwards, or is a straight line (on log paper?) drawn through a splash of points? I cannot accept the idea even of a singularity.

Cat

I think one of the biggest problems of black hole theory is thinking of black holes having mass from matter.
Matter beyond the nuclear force can't exist so for sure if we can't have matter we can't have density of matter.
Reason i think of black holes as no more that a time well of ever shrinking space/activity.

Black holes IMO are full of onion skin layers of ever decreasing well of time/activity.
Mass effect just that effect on regional space.
Density converted to lack of time/activity or lack of empty space for things to happen.