Physicists calculate proton's pressure distribution for first time

Physicists calculate proton’s pressure distribution for first time
MIT physicists have calculated the pressure distribution inside a proton for the first time. They found the proton’s high-pressure core pushes out, while the surrounding region pushes inward. Credit: Massachusetts Institute of Technology

Neutron stars are among the densest-known objects in the universe, withstanding pressures so great that one teaspoon of a star's material would equal about 15 times the weight of the moon. Yet as it turns out, protons—the fundamental particles that make up most of the visible matter in the universe—contain even higher pressures.

For the first time, MIT physicists have calculated a 's pressure distribution, and found that the particle contains a highly pressurized core that, at its most intense point, is generating greater pressures than are found inside a neutron star.

This core pushes out from the proton's center, while the surrounding region pushes inward. (Imagine a baseball attempting to expand inside a soccer ball that is collapsing.) The competing pressures act to stabilize the proton's overall structure.

The physicists' results, published today in Physical Review Letters, represent the first time that scientists have calculated a proton's pressure distribution by taking into account the contributions of both quarks and gluons, the proton's fundamental, subnuclear constituents.

"Pressure is a fundamental aspect of the proton that we know very little about at the moment," says lead author Phiala Shanahan, assistant professor of physics at MIT. "Now we've found that quarks and gluons in the center of the proton are generating significant outward pressure, and further to the edges, there's a confining pressure. With this result, we're driving toward a complete picture of the proton's structure."

Shanahan carried out the study with co-author William Detmold, associate professor of physics at MIT.

Remarkable quarks

In May 2018, physicists at the U.S. Department of Energy's Thomas Jefferson National Accelerator Facility announced that they had measured the proton's pressure distribution for the first time, using a beam of electrons that they fired at a target made of hydrogen. The electrons interacted with quarks inside the protons in the target. The physicists then determined the pressure distribution throughout the proton, based on the way in which the electrons scattered from the target. Their results showed a high-pressure center in the proton that at its point of highest pressure measured about 1035 pascals, or 10 times the pressure inside a neutron star.

However, Shanahan says their picture of the proton's pressure was incomplete.

"They found a pretty remarkable result," Shanahan says. "But that result was subject to a number of important assumtions that were necessary because of our incomplete understanding."

Specifically, the researchers based their pressure estimates on the interactions of a proton's quarks, but not its gluons. Protons consist of both quarks and gluons, which continuously interact in a dynamic and fluctuating way inside the proton. The Jefferson Lab team was only able to determine the contributions of quarks with its detector, which Shanahan says leaves out a large part of a proton's pressure contribution.

"Over the last 60 years, we've built up quite a good understanding of the role of quarks in the structure of the proton," she says. "But structure is far, far harder to understand since it is notoriously difficult to measure or calculate."

A gluon shift

Instead of measuring a proton's pressure using particle accelerators, Shanahan and Detmold looked to include gluons' role by using supercomputers to calculate the interactions between quarks and gluons that contribute to a proton's pressure.

"Inside a proton, there's a bubbling quantum vacuum of pairs of quarks and antiquarks, as well as gluons, appearing and disappearing," Shanahan says. "Our calculations include all of these dynamical fluctuations."

To do this, the team employed a technique in physics known as lattice QCD, for quantum chromodynamics, which is a set of equations that describes the , one of the three fundamental forces of the Standard Model of particle physics. (The other two are the weak and electromagnetic force.) The strong force is what binds quarks and gluons to ultimately make a proton.

Lattice QCD calculations use a four-dimensional grid, or lattice, of points to represent the three dimensions of space and one of time. The researchers calculated the pressure inside the proton using the equations of Quantum Chromodynamics defined on the lattice.

"It's hugely computationally demanding, so we use the most powerful supercomputers in the world to do these calculations," Shanahan explains.

The team spent about 18 months running various configurations of quarks and gluons through several different supercomputers, then determined the average pressure at each point from the center of the proton, out to its edge.

Compared with the Jefferson Lab results, Shanahan and Detmold found that, by including the contribution of gluons, the distribution of pressure in the proton shifted significantly.

"We've looked at the gluon contribution to the pressure distribution for the first time, and we can really see that relative to the previous results the peak has become stronger, and the pressure distribution extends further from the center of the proton," Shanahan says.

In other words, it appears that the highest pressure in the proton is around 1035 pascals, or 10 times that of a neutron star, similar to what researchers at Jefferson Lab reported. The surrounding low-pressure region extends farther than previously estimated.

Confirming these new calculations will require much more powerful detectors, such as the Electron-Ion Collider, a proposed particle accelerator that physicists aim to use to probe the inner structures of protons and neutrons, in more detail than ever before, including gluons.

"We're in the early days of understanding quantitatively the role of gluons in a proton," Shanahan says. "By combining the experimentally measured contribution, with our new calculation of the gluon piece, we have the first complete picture of the proton's pressure, which is a prediction that can be tested at the new collider in the next 10 years."


Explore further

First measurement of subatomic particle's mechanical property reveals distribution of pressure inside proton

More information: P. E. Shanahan et al. Pressure Distribution and Shear Forces inside the Proton, Physical Review Letters (2019). DOI: 10.1103/PhysRevLett.122.072003 , journals.aps.org/prl/abstract/ … ysRevLett.122.072003
Journal information: Physical Review Letters

This story is republished courtesy of MIT News (web.mit.edu/newsoffice/), a popular site that covers news about MIT research, innovation and teaching.

Citation: Physicists calculate proton's pressure distribution for first time (2019, February 22) retrieved 16 July 2019 from https://phys.org/news/2019-02-physicists-proton-pressure.html
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Feb 22, 2019
"1035 pascals," ?? (Twice)
10 ^ 35 surely...

Feb 22, 2019
Confirming these new calculations
.........and keep this uppermost in mind.

will require much more powerful detectors, such as the Electron-Ion Collider, a proposed particle accelerator
.....which in all likelihood will never be built because the LHC in Cern is already beset with unconfirmed predictions as to QUARK theory & what they hoped would come out of that which has never come to fruition.

Proving QUARK theory is fundamental to all these "calculations". Until the first quark is isolated none of the calculations discussed in the article mean a thing.

I wonder how many in the Pop-Cosmology clan living in this chatroom think QUARKS have already been isolated & thus proven to exist? Yeah, they'll just go off in a rant with the usual Pop-Cosmology psycho-babble stuff about EFFECTS,


Feb 22, 2019
Until the first quark is isolated none of the calculations discussed in the article mean a thing.


Quarks cannot be isolated due to confinement you ignoramus.

Feb 22, 2019
So it's a bit like the thermal equilibrium of a star?

Feb 22, 2019
Meanwhile the spent radioactive 'fuel rods' are stacking up blocking the doorways to the nuke facilities in our land of the hubristic.

Feb 22, 2019
"....one teaspoon of a [neutron] star's material would equal about 15 times the weight of the moon"

Huh?

Feb 22, 2019
The analyses need to be repeated, taking all particles into consideration. With one other consideration or two. There are insufficiently understood physical interactions at all levels with regard to consideration of the third and higher derivatives of the standard equation of motion in its practical multidimensionality. And this should include three dimensions of time, not just one that describes our path which is a resolution of the three temporal actual dimensions of time into a resultant vector which is misleading. Misleading because the functions, partial differential and whole differential multivariable functions individually describing the three constituent temporal subvectors up to now get devalued or assumed because of up to now the difficulty within QCD of working with them. Now we are beginning to be able to model some of this with the advances of supercomputers progressively every year. Recognizing such frees us from temporal causality issues to a large extent.

Feb 22, 2019
" Until the first quark is isolated none of the calculations discussed in the article mean a thing. "

As usual the realistic voice in the crowd gets downvoted, just wanted to say well said Benni. Pop science with math as the only validation is getting pretty insane these days. As are it's supporters. Although that is understandable.... when the only verification that what you believe is real is provided by a calculator display.

Feb 22, 2019
They shared all assumptions made, and the logic behind them. So I don't know why you all have your panties in a bunch, what are they supposed to do...not reveal any of their work until it is 100% complete and proven by both math and observation? If scientists took that approach Einstein would have taken his work to the grave.

Feb 22, 2019
"Inside a proton, there's a bubbling quantum vacuum of pairs of quarks and antiquarks, as well as gluons, appearing and disappearing,"

As a person who really only understands f=ma, I must say that is astounding. And inside the quarks, higher pressures still? Or maybe they are hollow?

Feb 23, 2019
@Benni,

Just because you can't see a quark or a black hole doesn't mean it isn't there. There are ways of confirming existence other than direct observation; environmental observations, measurements, mathematics, logic, and consistency.

I can't see a magnetic field line, but I can make observations and measurements, do some mathematics, apply logic, and see that consistency shows me it's there.

Do you see anything wrong with that, @Benni? If not, why are you so closed-mindedly opposed to black holes and quarks that no evidence, direct or otherwise, will convince you?

Quarks and black holes are excellent explanations for certain phenomena with a great deal of evidence for their existence; if later evidence indicates they don't exist, that's fine, too; I'll be fascinated. But evidence, please, @Benni; not simple opposition supported by loud denials, only.

Try science, @Benni, not brute-headed opposition for no good reason.

Feb 23, 2019
Prefer QED representation. Also, "gluons" and "gravitons" can't actually be seriously considered.

Feb 23, 2019
@theredpill,

"Calculator display"?

No wonder you're behind in your understanding.

Feb 23, 2019
When we truly split this Atom

We've isolated the Neutron, the Proton, and the Electron
but
that is only seperating this atoms nucleons
because
the Neutron decays naturally into a Proton, Electron, Neutrino and gamma ray
we haven't truly split this atom
so
to truly split this atom
is
When we split this Proton
because
we have never observed this Protons innards intact naturally

When we split this Proton
and
observe these theoretical Quarks
then these will no longer be theoretical Quarks
then
we can say
We have truly split this Atom

Feb 23, 2019
Just because you can't see a quark or a black hole doesn't mean it isn't there. There are ways of confirming existence other than direct observation; environmental observations, measurements, mathematics, logic, and consistency.
.........standard Pop-Cosmology psycho-babble when you guys are promoting your fantasies.

You imagine "effects" infers the existence of dark matter as well. Dark matter is "inferred", gravity is not "inferred" because we already KNOW it's what keeps your feet planted on a solid terrestrial Earth.


Feb 23, 2019
Just because you can't see a quark or a black hole doesn't mean it isn't there. There are ways of confirming existence other than direct observation; environmental observations, measurements, mathematics, logic, and consistency.
.........standard Pop-Cosmology psycho-babble when you guys are promoting your fantasies.

You imagine "effects" infers the existence of dark matter as well. Dark matter is "inferred", gravity is not "inferred" because we already KNOW it's what keeps your feet planted on a solid terrestrial Earth.



Clueless tosser.

Feb 23, 2019
Contrary to what this article claims, Protons aren't fundamental.

Feb 23, 2019
Contrary to what is claimed in this article, Protons have no outer edge.

Feb 23, 2019
I wonder how many in the Pop-Cosmology clan living in this chatroom think QUARKS have already been isolated" - Benni

Poor Benni. He doesn't seem to understand the difference between the very big and the very small.

Feb 23, 2019
The concept of pressure has no applicability to the interior of protons.

For one thing, protons have no defined "interior" or extent. They aren't little balls.

Feb 23, 2019
@Benni,

Why do you keep pretending you know something about physics?

With respect to "dark matter," it is obvious something is there; as no one knows what, and it acts like it has gravity, it has been given the placeholder name, "dark matter." It's like using x in an equation. We are slowly learning how it behaves; we don't know what it is.

Every time you type, you demonstrate you know nothing; unlike a real physicist, you won't admit it. When you don't understand something, you call it "Pop-Cosmology." That's funny, because it's what real, serious, reputable, cosmologists do, yet you know more than they do. That's funny.

Feb 23, 2019
"@Benni,

Why do you keep pretending you know something about physics?"

It is the same reason why Trump thinks he knows something about being president. It is a combination of profound ignorance and mental illness.

It is no coincidence that he is also a Mad MAGA hatter.

Feb 23, 2019
This comment has been removed by a moderator.

Feb 23, 2019
I know @Benni's clueless, and I'm not surprised he's a Mad MAGA Hatter, but I cannot resist trying to teach him something. As a retired professor and researcher, I simply cannot help myself, even if it's hopeless.

I'm an eternal optimist.

Feb 23, 2019
@Benni,

Every time you type, you demonstrate you know nothing; unlike a real physicist, you won't admit it. When you don't understand something, you call it "Pop-Cosmology."
......you read over the rest of it: "Pop-Cosmology psycho-babble", I'm better than you are at completing my own text.

Feb 25, 2019
"it appears that the highest pressure in the proton is around 1035 pascals, or 10 times that of a neutron star, similar to what researchers at Jefferson Lab reported."

Awesome test, seems we really do know what we are doing here!

Also, neutron stars seems to be well named, there really should be identifiable neutrons throughout (except for the outer layers perhaps).

"Inside a proton, there's a bubbling quantum vacuum of pairs of quarks and antiquarks, as well as gluons, appearing and disappearing,"

As a person who really only understands f=ma, I must say that is astounding. And inside the quarks, higher pressures still? Or maybe they are hollow?


No, protons are composite particles, and quarks are resonant ripples (particles) of a quantum field so with wavelength (and charges, masses, spins et cetera) but no internal pressure. - tbctd -

Feb 25, 2019
- ctd - The proton (and neutron) masses are famously not much of the constituent almost always present "valence" quarks, but a sea of "virtual particle" - quasi stable ripples - quark and gluon matter/antimatter pairs that are constantly made and destroyed as result of the relativistic energy from the "valence" particles. They are highly energetic since the strong force counter intuitively lets them be most free when they are confined in a small volume ("asymptotic freedom") - small volume, high energy.

Contrary to what this article claims, Protons aren't fundamental.


Your comments are mostly erratic, this is perhaps touching on something tangible. But the article likely thought of them as fundamental for atoms, not as quantum fields. Potato, potatoe.

Feb 26, 2019
The concept of pressure has no applicability to the interior of protons.
"Their results showed a high-pressure center in the proton that at its point of highest pressure measured about 1035 pascals, or 10 times the pressure inside a neutron star."

Or probably the interior of a neutron star. Energy density would be a better term.

Feb 26, 2019
cont
The energy density inside a neutron star would actually probably be less than that of the surrounding spacetime. Because the neutrons displace spacetime which generates virtual particles. The creation of these particles produce the actual pressure compressing the neutron star. Matter caught up in this pressure differential experiences what appears as gravity. The energy density of protons actually increases from the center until it reaches normal spacetime density around the proton. In this view it acts similar to a black hole only I don't think you could define an event horizon.

Feb 26, 2019
Pop-Cosmology psycho-babble


Translated: "Something I don't understand, and therefore scares me."

Feb 26, 2019
@MrBojangles,

Pop-Cosmology psycho-babble


Translated: "Something I don't understand, and therefore scares me."


You got it.

@Benni: "Pop-Cosmology" and "Pop-Cosmology psycho-babble" are the same thing -- your posts.

Mar 01, 2019
This mighty Proton

This electron can stand 10x the pressure than a neutron star
as
now it seems
Protons can stand 10x the pressure than a neutron star
10x the pressure is greater than when a neutron star forms a blackhole
as
a blackhole cannot have a diameter smaller than 3km
as its internal pressure cannot be greater than its light radius
means
a blackholes internal pressure cannot be greater than 10x the pressure of a neutron star
because
it follows the formula R = 2GM/C² where its gravity is zero at its centre of mass
all this means
these protons and electrons exert a greater pressure than inside a blackhole
Meaneth protons and electrons exist in blackholes
as they exist outside blackholes

Mar 01, 2019
it follows the formula R = 2GM/C² where its gravity is zero at its centre of mass
all this means
these protons and electrons exert a greater pressure than inside a blackhole
Meaneth protons and electrons exist in blackholes
as they exist outside blackholes


But granDy, that isn't what they tell us about BH birth pangs.

They tell us to believe BHs are born from neutron stars, thus BHs are in essence neutron stars even more compact & denser than they were before their BH birth. So how did they get so dense if there is no gravity at their centers in accordance with the Inverse Square Law?

Mar 01, 2019
This defining nucleon pressure

When formulating theories, Benni
make sure their interchangeable
because we're not connecting the dots, so as to prove our other theories
a quark is not seen outside a proton
a proton exist inside a blackhole
meaning
a quark gluon plasma does not exist inside a blackhole
why
because protons exist as protons at greater pressures than neutron stars and blackholes
because the proton pressure is too great to split the proton in blackholes
which impinges on
the degenerate neutron theory
the proton is held together with the speed of light
Gravities light radius cannot break the proton

Mar 01, 2019
They tell us to believe BHs are born from neutron stars,
And @Benni lies again.

Mar 01, 2019
@Benni,

Who said black holes are born from neutron stars?

No astrophysicist I know ever said that.

Explain how a black hole is born from a neutron star -- that's something I don't know.

Mar 01, 2019
@Benni,

Who said black holes are born from neutron stars?

No astrophysicist I know ever said that.

Explain how a black hole is born from a neutron star -- that's something I don't know.
.......me neither, but that's what Pop-Cosmology keeps telling the gullible, I'm just not one of the gullible, I know a lot of nuclear physics & neutron stars ain't in that picture.

Mar 02, 2019
@Benni,

You just confirmed you don't know enough nuclear physics, because neutron stars are out there -- pulsars and magnetars. They'll kill you if you get too close to them. Plus, there's the magnetar that blew away part of our stratosphere in late 2004 when it shuddered about 50,000 years ago. Magnetars are dangerous, even from very, very far away.

Your Pop-Cosmology says black holes come from neutron stars; astrophysicists don't.

Will you ever learn, @Benni?

Mar 02, 2019
This is why blackholes attached themselves to singularities
Benni> They tell us to believe BHs are born from neutron stars thus BHs are in essence neutron stars even more compact & denser than they were before their BH birth So how did they get so dense if there is no gravity at their centers in accordance with the Inverse Square Law

Because
mathematically the centre is infinitely small
this allowed infinite gravity
infinite density
but
when LIGOs GW170817 emerged
this is when R = 2GM/C² emerged where R = the velocity of light hence Gravities Light Radius
as only a star has sufficient mass to create a blackhole or Light Radius Star
when Jocelyn Bell Burnell discovered the first pulsar
the pulsar became the intermediate step for blackholes or Light Radius Stars
as
theories impinge on existing theories
the theoretical non spinning blackhole as a pulsar was immediately up the spout
because
GW170817 is two orbital neutron stars

Mar 02, 2019
"Their results showed a high-pressure center in the proton that at its point of highest pressure measured about 1035 pascals, or 10 times the pressure inside a neutron star."
Not withstanding my contention that the pressure outside an atom is greater that that within (similar to black holes), this observation should be no great surprise since to eject a proton from the atom you would first have to insert an electron to neutralize its charge and make it into a neutron.

Mar 02, 2019
...quarks are resonant ripples (particles) of a quantum field so with wavelength (and charges, masses, spins et cetera) but no internal pressure. - tbctd -
Note quarks have mass but no internal pressure. Sort of like black holes? Wondering if Einstein ever actually used the words "infinite density" or if people have just been putting words in his mouth. Something that an academic physicist should know I would think.

Mar 02, 2019
...quarks are resonant ripples (particles) of a quantum field so with wavelength (and charges, masses, spins et cetera) but no internal pressure. - tbctd -
Note quarks have mass but no internal pressure. Sort of like black holes? Wondering if Einstein ever actually used the words "infinite density" or if people have just been putting words in his mouth. Something that an academic physicist should know I would think.
....he NEVER used the words "infinite density", it's Pop-Cosmology that introduced their claims that this is what Einstein meant, in other words that Einstein needed someone smarter than he was to speak for his inability to say what he meant.

Mar 02, 2019
@Benni,

No one, except you, I think, has equated infinite density with infinite mass or infinite gravity. Infinite density occurs when either an infinite or a finite mass is condensed into zero volume. It's still the same mass. Ten kilograms of mass condensed to zero volume has infinite density, but is still only ten kilograms; you could still support its weight in your hand. By the same token, one kilogram of mass condensed to zero volume has infinite density, but is still only one kilogram. If it can be condensed down to zero volume, any finite mass can have infinite density; it won't have infinite gravity.

Density and mass are two entirely different things. A piece of styrofoam with a mass of ten kilograms won't have nearly the density of a piece of lead with a mass of ten kilograms. Each contains the same amount of mass, but in one, the density of that mass is far greater than in the other.

For any finite mass, as volume approaches zero, density increases without bound.

Mar 02, 2019
No one, except you, I think, has equated infinite density with infinite mass or infinite gravity. Infinite density occurs when either an infinite or a finite mass is condensed into zero volume.
.....well here it is directly from your favorite textbook:

https://en.wikipe...ack_hole

Singularity
Main article: Gravitational singularity

"At the center of a black hole, as described by general relativity, lies a gravitational singularity, a region where the spacetime curvature (gravity) becomes infinite. For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density."


Mar 02, 2019
Note quarks have mass but no internal pressure. Sort of like black holes?
If so, you would have mass, no pressure, and infinite density for quarks and black holes. At least for black holes anyway. I'd rather say no mass, no internal pressure, and no infinite density. But we know black holes have mass because they have gravity, don't they? Problem is we need to ditch our sacred theories about gravity and realize gravity comes from a gradient in the energy density of spacetime. Same mathematics for general relativity but a different interpretation of the variables. No more marbles rolling around in bowls to illustrate gravity in the children's museum. Hopefully people won't think we've lost our marbles. Anyway the singularity represents a discontinuity in the energy density of spacetime. Like region A has density 1 and region B has density 0. The density gradient at the singularity is 1/0. No infinite densities involved.

Mar 02, 2019
@Benni,

.....well here it is directly from your favorite textbook:

https://en.wikipe...ack_hole

Singularity
Main article: Gravitational singularity

...It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density."



Uh, you're still having trouble reading: "...the singular region contains all the mass of the black hole solution."

That's finite mass, @Benni, not infinite mass. Finite mass, in zero volume, has infinite density. It's still a finite mass. No black hole has infinite mass.

It does not have infinite gravity, as it does not have infinite mass. It's rate of change of gravity becomes infinite near the singularity.

Learn to read! It's no wonder you can't learn.

You are almost infinitely wearying; you are infinitely dense.

Wikipedia is not my favorite textbook. I prefer scientific articles. I've also written some.

Mar 02, 2019
Wikipedia is not my favorite textbook. I prefer scientific articles. I've also written some.
then you write:

Uh, you're still having trouble reading: "...the singular region contains all the mass of the black hole solution."

That's finite mass, @Benni, not infinite mass. Finite mass, in zero volume, has infinite density. It's still a finite mass. No black hole has infinite mass.

It does not have infinite gravity, as it does not have infinite mass. It's rate of change of gravity becomes infinite near the singularity.
,,,,,,how does "rate of change of gravity become infinite"?

You spend almost all your time here re-explaining Pop-Cosmology theories so as to make them sound as if they don't really say what they plainly do say, "infinite rate of change", what psycho-babble.

How about some fantasy psycho-babble explanation about how ANYTHING can go through an infinite rate of change.

Mar 02, 2019
@Benni,

You've just proven you know nothing about physics and mathematics.

Gravity changes as you move away from a source. The closer you are, the greater the gravity; the further away you are, the less the gravity. The rate of change in gravity with respect to distance can be plotted.

If a gravitational source is a true point source -- a singularity -- that means the rate of change of its gravitational field will approach infinity the closer you get to that point source. You can actually never get there, mathematically, but the closer you get, the slope of the rate of change of its gravitational field will get closer and closer to vertical when plotted. Any rate of change curve that asymptotically approaches a vertical line means it's becoming infinite. It's infinite only at the singularity, which actually isn't really anywhere, because the probability of landing on a single point anywhere in space-time is zero; it's also fuzzy.

Freshman college mathematics.

Mar 02, 2019
Uh, you're still having trouble reading: "...the singular region contains all the mass of the black hole solution."
Me too. The singularity is the drain. All the water goes down the drain and out the wormholes into the dark matter halo around the galaxy. Water being the energy content of matter. But the structure of the black hole remains intact. Like an empty shell. The structure maintains the separation between energy densities inside and outside the event horizon, so the BH doesn't lose its gravitational force. The more water goes down the drain, the more the shell builds up and the more the gradient of energy densities between regions inside and outside the BH, so the BH actually increases its gravity while redistributing its energy. At least for the super-massive black holes at the center of galaxies.

Mar 04, 2019
The more water goes down the drain, the more the shell builds up and the more the gradient of energy densities between regions inside and outside the BH, so the BH actually increases its gravity...
I don't think the gradient increases as the shell builds up. Rather the amount of spacetime exposed to the gradient increases which affects the gravitational force. Technically the singularity is a ring singularity which would scale as 2/3 the volume of the BH, Similarly the gravitational force. So you might say supermassive black holes would appear to be bloated. That is they become proportionately less effective as they grow. That would effectively limit their size. Anyway this hypothesis could be tested when we launch the telescope which can tell us more about their size.

Mar 04, 2019
cont
It seems likely the shell is maintained by the strong force which was holding nuclear material together that falls through the singularity. So we have a distinction between matter and dark matter - dark matter has lost its strong force. Also it's probably a good thing that bigger black holes lose their effectiveness because otherwise one might just take over most of all matter and there would only be all matter forming only one galaxy.

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