Something I don't get about density and black holes

[Lord Antares]

If you make an arragement of atoms in the tightest way possible, due to their shape (even though that term is very loose), there will be some gaps in matter, or ''micro-vacuums''. Therefore, there must be such a thing as the highest possible number of atoms that can be fit inside a space of certain dimensions before the nuclear force is broken down.

But the nuclear force can be broken down, something that happens when a black hole is forming.

 

To my understanding, the singularity of a black hole (if there is such a thing) is thought to be comprised of just matter with no gaps in structure. This would mean that the space it occupies is occupied in whole, without the possibility of it getting denser. If any more matter is added to it, its volume will grow but not its density. My question is, why is then ''maximum density'' not something that exists in physics? The singularity IS thought to have infinite density, but this is a result of the equation p = m/v where v = 0, hence p = infinite, and not what I am talking about.

 

Furthermore, if all singularities are the same size, how can some have more distant event horizons than others? You could say that some have more mass, but how could they have more mass if their size is zero and density infinite?

 

What piece of information am I missing? Thanks in advance for any helpful replies.

Edited May 25, 2017 by Lord Antares

[KipIngram]

I'm not expert in this area, but I have been trying to read up on quantum field theory, and I think your misstep is in regarding matter as ultimately something solid to start with. All of those particles that make up the atoms aren't really little balls - they're excitations of various fields, so the whole idea of trying to describe the space they "fill" in an intuition-based way just doesn't work, I think.

[DrP]

In a BH the whole thing has collapsed in on itself and has been compressed so that these gaps between the atoms are no longer there - thus the almost unfeasible density as it is like one giant super nucleus (or something else - but not normal atoms arranged as we would normally find them here).

 

That's how I have always visualised it anyway.... it's probably wrong - now maybe a proper space physicist can explain it properly. ;-)

[Lord Antares]

I'm not expert in this area, but I have been trying to read up on quantum field theory, and I think your misstep is in regarding matter as ultimately something solid to start with. All of those particles that make up the atoms aren't really little balls - they're excitations of various fields, so the whole idea of trying to describe the space they "fill" in an intuition-based way just doesn't work, I think.

 

I know this but I have been lead to believe that this is no longer true once a black hole forms, since there is no more repulsion between electrons, everything is squashed into pure matter.

 

 

In a BH the whole thing has collapsed in on itself and has been compressed so that these gaps between the atoms are no longer there - thus the almost unfeasible density as it is like one giant super nucleus (or something else - but not normal atoms arranged as we would normally find them here).

 

That's what I said.

[KipIngram]

"Pure matter" is still just excitation of fields.

[imatfaal]

If you make an arragement of atoms in the tightest way possible, due to their shape (even though that term is very loose), there will be some gaps in matter, or ''micro-vacuums''. Therefore, there must be such a thing as the highest possible number of atoms that can be fit inside a space of certain dimensions before the nuclear force is broken down.

But the nuclear force can be broken down, something that happens when a black hole is forming.

 

Even in a neutron star there are no atoms (or precious few) - the gravitational pressure is such that protons and electrons fuse via electron capture create neutrons. The whole star is neutrons held apart by neutron degeneracy pressure which is basically the outcome of the pauli exclusion principle

...

To my understanding, the singularity of a black hole (if there is such a thing) is thought to be comprised of just matter with no gaps in structure. This would mean that the space it occupies is occupied in whole, without the possibility of it getting denser. If any more matter is added to it, its volume will grow but not its density. My question is, why is then ''maximum density'' not something that exists in physics? The singularity IS thought to have infinite density, but this is a result of the equation p = m/v where v = 0, hence p = infinite, and not what I am talking about.

 

the Singularity is something which is predicted in General Relativity (Hawking and Penrose) - but the existence of the singularity is normally taken as a sign that beyond event horizon is out of scope for GR; ie you need a new theory to properly deal with this.

...

Furthermore, if all singularities are the same size, how can some have more distant event horizons than others? You could say that some have more mass, but how could they have more mass if their size is zero and density infinite?

 

What piece of information am I missing? Thanks in advance for any helpful replies.

 

"What piece of information am I missing?" That we know next to nothing about what happens behind the event horizon and definitely not what is going on at the singularity - or possibly more accurately, and definitely not what is actually there instead of a physical singularity

[Strange]

We probably need a theory of quantum gravity to answer this. String theory predicts a fuzzball.

https://en.m.wikipedia.org/wiki/Fuzzball_(string_theory)

[imatfaal]

"Pure matter" is still just excitation of fields.

 

Let's keep QFT out of this thread apart from where essential - and also bear in mind that QFT is a tool for understanding what we observe and not necessarily the undiluted/unsullied truth of nature (like all scientific models)

[Lord Antares]

"What piece of information am I missing?" That we know next to nothing about what happens behind the event horizon and definitely not what is going on at the singularity - or possibly more accurately, and definitely not what is actually there instead of a physical singularity

 

Aha, so my reasoning is not irrational here? I thought I was being purely speculative.

 

Actually, the piece of information I was missing is this:

 

 

the Singularity is something which is predicted in General Relativity (Hawking and Penrose)

 

I heard about this but am not familiar with the details. Is it possible at all to explain to a layman how these paradoxes were inferred from relativity? I assume the mathematics of it cannot be put into simple form since they must be complicated, judging by the fact it took so many years to figure it out.

 

 

 

Even in a neutron star there are no atoms (or precious few) - the gravitational pressure is such that protons and electrons fuse via electron capture create neutrons. The whole star is neutrons held apart by neutron degeneracy pressure which is basically the outcome of the pauli exclusion principle

 

Fascinating information. I will look the pauli exclusion principle up.

But they are still formed in a structure-like manner like regular matter is, rather than being one consistent piece of matter like the singularity is supposed to be, right?

[Strange]

The structure of neutron stars is complex and fascinating. I seem to remember lots of pasta analogies (spaghetti, lasagna etc)

[imatfaal]

The structure of neutron stars is complex and fascinating. I seem to remember lots of pasta analogies (spaghetti, lasagna etc)

 

- The pasta thing made me remember a good page for Neutron Stars

 

Anyway, imagine starting at the surface of a neutron star and burrowing your way down. The surface gravity is about 10^11 times Earth's, and the magnetic field is about 10^12 Gauss, which is enough to completely mess up atomic structure: for example, the ground state binding energy of hydrogen rises to 160 eV in a 10^12 Gauss field, versus 13.6 eV in no field. In the atmosphere and upper crust, you have lots of nuclei, so it isn't primarily neutrons yet. At the top of the crust, the nuclei are mostly iron 56 and lighter elements, but deeper down the pressure is high enough that the equilibrium atomic weights rise, so you might find Z=40, A=120 elements eventually. At densities of 10^6 g/cm^3 the electrons become degenerate, meaning that electrical and thermal conductivities are huge because the electrons can travel great distances before interacting.

 

Deeper yet, at a density around 4x10^11 g/cm^3, you reach the "neutron drip" layer. At this layer, it becomes energetically favorable for neutrons to float out of the nuclei and move freely around, so the neutrons "drip" out. Even further down, you mainly have free neutrons, with a 5%-10% sprinkling of protons and electrons. As the density increases, you find what has been dubbed the "pasta-antipasta" sequence. At relatively low (about 10^12 g/cm^3) densities, the nucleons are spread out like meatballs that are relatively far from each other. At higher densities, the nucleons merge to form spaghetti-like strands, and at even higher densities the nucleons look like sheets (such as lasagna). Increasing the density further brings a reversal of the above sequence, where you mainly have nucleons but the holes form (in order of increasing density) anti-lasagna, anti-spaghetti, and anti-meatballs (also called Swiss cheese).

 

Taken from here M Coleman Miller's Introduction to Neutron Stars

[DrP]

So! The moon isn't made of cheese.... but a neutron star maybe? :-D

[imatfaal]

I heard about this but am not familiar with the details. Is it possible at all to explain to a layman how these paradoxes were inferred from relativity? I assume the mathematics of it cannot be put into simple form since they must be complicated, judging by the fact it took so many years to figure it out.

That mathematical singularities ("divide by zero error" ) existed was known very soon - use of Schwarzchild Coordinates at the Event Horizon to give stopped time is a common example. But these involved calculational procedures that might be wrong. It was also known that certain unphysical scenarios would lead to physical singularities - but doubted whether any of these would actually manifest. Hawking showed they happned in actuality

This is not a good page - but I am struggling to find one. https://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems

This is interesting but does not help that much https://quantumfrontiers.com/2014/11/05/the-science-that-made-stephen-hawking-famous/

[Lord Antares]

Thanks for the links. While much of it went over my head, I was able to understand some things. I will come back if I have more questions.

 

 

We probably need a theory of quantum gravity to answer this. String theory predicts a fuzzball.
https://en.m.wikipedia.org/wiki/Fuzzball_(string_theory)

 

Don't think I ignored this. It's just that I know nothing about String theory and can't make anything of this.

[Strange]

Don't think I ignored this. It's just that I know nothing about String theory and can't make anything of this.

Same here. It's just one of those bits of String Theory Trivia that I have picked up.

[MigL]

There are three stages to stellar collapse.

When a star of a certain mass collapses, it mostly consists of ionized nuclei, from hydrogen up to iron, plus a bunch of free electrons. These electrons, being fermions, are subject to electron degeneracy pressure ( see the Pauli exclusion principle ). It is this electron degeneracy pressure which keeps the white dwarf star from further collapse.

What happens to the star if it has more mass than that certain amount, or if you add mass to it ?

Electron degeneracy is no longer able to resist the relentless squeeze of gravity, and the electrons are constrained to a very small volume. According to the Heisenberg Uncertainty Principle, when you fix the position of an electron, its momentum can vary wildly, so much so that its speed ( momentum= mass x speed ) can be greater than c , which is obviously unphysical.

The electrons get around this problem by merging with protons to make neutrons. Since neutrons are three orders of magnitude heavier than electrons, their speed can be three orders of magnitude less for the same momentum. I.E. the neutrons can be constrained to a smaller volume than electrons without becoming unphysical. As you add more mass, eventually the resisting force becomes neutron degeneracy ( again see the Pauli Exclusion Principle ), with the neutrons arranged in various configurations along the way ( see Imatfaal's previous post ).

What happens if you add even more mass ?

Eventually neutron degeneracy can no longer restrain gravity, but we currently know of no force or mechanism which will stop the collapse, and the star will shrink to a dimensionless point ( singular ). This is again, unphysical, so no-one actually thinks this happens. We don't have a valid theory which describes the situation, and observations are impossible, since nature throws up an event horizon that prevents us from ever observing what happens after collapse past a certain point.

The hope is that a theory of quantum gravity will make the unphysical singularity of GR redundant, and make some predictions which make a little more sense.

[KipIngram]

MigL, that's very nice. Those few paragraphs taught me a ton.

[Mordred]

Excellent summary very accurate +1

 

very complete

Edited May 26, 2017 by Mordred