Shell Universe

[ExpEarth]

I'm happy to report that my shell cosmology model was finally published after a whole year of rejections. Here is the link:

https://www.mdpi.com/2674-0346/3/3/14

It is similar in many ways to the preprint I discussed in #204. However, I found recent findings from GR that gave strong support to the shell conjecture. The new GR findings consist of new solutions for the equations of state of neutron stars and compact objects, originally found by Jun Ni. Others have followed up on this. Basically, the old idea of what the inside of these objects looks like is transformed. There would instead be a central void of matter and a repulsive gravitational field centred on the origin. I link the Hubble redshift to the gravitational field induced by the shell in Ni's approach. Unlike the model in #204, the shell of the new model is very thick, about one-half or one-third the size of the observable universe.

Thanks to all, especially Louis, for the all the valuable discussions here in AGC.

[RedshiftDrift]

Congratulations @ExpEarth for your publication!
I am happy to see how discussions on the ACG forum helped you re-evaluate and adjust your ideas.
Thanks for acknowledging our discussions from a long time ago...

The Ni redshift could replace Gupta’s TL redshift in this approach while avoiding the problems of TL models

Gupta uses the assumption of an isotropic and homogeneous mass distribution, and adjusts how the physical constants must vary in time so that the TL model will fit with the rest. The Ni redshift cannot replace TL redshift in Gupta's model without breaking the other assumptions of that model.

... the problems of TL models

What problems of TL models? 😄

[ExpEarth]

Thanks @RedshiftDrift . I'm sure I would not be as far along without AGC. It's not just the huge amount of new information but also the energy and interest of all the members.

Regarding the connection with Gupta's model, it was not so much that I was trying to rescue his model. I don't really like it that much and don't give it much chance. But Gupta's approach of using TL in a hybrid model with LCDM is golden. It allows alternative ideas to be communicated to the mainstream. Probably 95% of cosmologists favour LCDM to the extent that they can't even understand attempts to replace it.

The problems of TL models we have discussed often here. The main ones that come to mind are the blurriness problem (there was a discussion with that title), the problem of supernova time dilation and of course the temperature-redshift relation in the CMB. In my model, the Hubble redshift is a gravitational redshift and so the time dilation arises naturally. The CMB temperature distribution if consistent with a shell configuration with energy loss.

Now I should point out that my model is also a TL model in this unusual sense: the gravitational redshift is actually a TL redshift. How? The energy that is lost in the gravitational redshift is what goes into driving masses together in gravitation. That connection did not make it into the published version.

[HanDeBruijn]

Cosmological Principle / Preferred Origin

@ExpEarth writes in his article:

One objection to a Ni shell universe is that it violates the Cosmological Principle and even imposes a geo-centric view. Yet the increasing discoveries of anisotropies and nonuniformities, such as in quasar counts, CMB polarization and mass distribution, including the KBC [Keenan–Barger–Cowie] Void, collectively imply that this principle is no longer a valid assumption.

Dismissed. People have often forgotten what proper mathematical modelling is, mathematical modelling as it should be. What follows is a quote from the webpage named Square Bubbles:

the beauty of the formula found is due only to the dramatic simplification that we have applied. The beauty does not occur because we have grasped the reality in all its details, but precisely because we have dispensed of most aspects of reality, not because we have pursued the whole truth, but precisely because we have not pursued that truth. The paradox is that we nevertheless have come closer to "the truth". After all, the result is quantitative, agrees well with the experiments, in short: is exactly what one would expect of a (small) piece of science.

Returning to the article:

Supposing the Milky Way lies very close to the origin of the shell, within the KBC Void

There is an extremely simple formula for the Pioneer anomaly, which is found by "wrongly" assuming that the whole universe is at one side of our solar system. Nevertheless it is a "good" model for the Void we are living in. It is a model as it would have been set up for a real world problem by an engineer. Resulting in the following estimate.

$$ \large a_P = \kappa cH $$

where $a=$ anomalous acceleration, $c=$ speed of light, $H=$ Hubble parameter and $0.375\lt \kappa\lt 2$ is a pure number.

We next address the stellar blueshift problem that arises in a Ni shell universe. As mentioned earlier, unless the Milky Way were positioned at the exact origin of the shell universe, there should be some stars closer to the origin than we are that would exhibit a Ni blueshift as seen by us. Since such a pattern has not been observed, this presents a serious obstacle to a Ni shell universe which must first be resolved.

It is noticed in general that the Variable Mass Theory does not have a preferred origin. The origin of the VMT Black Hole Universe travels along with the observer. Any observing civilization has an such an origin moving with it, as if their Milky Way were positioned at the exact origin of the accompanying Observable Universe.

[ExpEarth]

Thanks for having a look at my paper, Han, and for your interesting comments. I'm not following you on your first comment related to the possibility of a somewhat geocentric universe.

But what you said about the Pioneer acceleration could be quite relevant. I'm aware of that old idea that the Pioneer acceleration and the Hubble redshift might be caused by the gravitational effect of a universal half sphere. Of course this has been a hard idea to like because in an endless universe we would expect the gravitational forces to cancel out at any given point in space. This also appeared to hold true in the case that the universe has a shell configuration, as I had proposed. Whether you look at it in Newtonian gravity or GR, the gravitational forces at any point inside the spherical shell, arising from the shell itself, should be zero. I had supposed this was a merit of the shell approach, but it turned out I was likely wrong on that. The relativistic Ni solutions in GR rule out a flat Minkowski space inside. The gravitational forces inside do not cancel out and so a mass at a point inside the sphere will be attracted to the section of the shell nearest to it. DeLyra describes this effect as a repulsive gravitational field centred on the origin. Neslusan tells me that it is better to describe it as just an extra attraction of the nearby shell section. The math is all heavy Einstein field equations.

The net result of all this is that the idea that the Pioneer anomaly and the Hubble redshift are due to attraction of the cosmic half sphere becomes plausible. Using the thin-shell ('eggshell') approximation, and supposing we are near the centre of the shell, then the mass of the section of shell closest to us might be something like M/4. So the gravitational force of this section at our position is F = GMm/4R^2 , where R is the Hubble radius = c/H . Now since we are supposing the universe to be in the form of a black hole, we can express the mass in terms of the radius by the black hole mass-radius relationship M = Rc^2/2G . So the force then becomes F = mc^2/8R = mcH/8 (since R = c/H ). The quantity cH has the units of acceleration and its numerical value, similar to G , is close to the Pioneer and MOND accelerations.

It makes me wonder about the other spacecraft and their anomalous accelerations. They did not all show the Pioneer one and maybe this could reflect the different directions they were moving in.

[HanDeBruijn]

the mass of the section of shell closest to us might be something like M/4.

If instead of your M/4 twice that amount of mass or even the whole mass is assumed then we get for the anomalous acceleration of the Pioneer roughly the same result as in my comment.

$$ a_P = \frac{F}{m} = \kappa Hc \quad \mbox{with} \quad 0.25 \le \kappa\le 0.5 \quad \mbox{instead of} \quad 0.375\le \kappa\le 2 $$

But your calculation has the advantage that it is much simpler !!

Quite in general I was asking myself last night (again) how comes that our seemingly very different models nevertheless lead to similar results. And I think I found sort of an explanation. Sketched in the graph below.

The Shell universe has a sharp boundary, it simply ends at a distance $R=c/H$ .
The Variable Mass universe has a "smooth boundary", extending to infinity, but with the same decay distance $R=c/H$ .
Thus Matt's step function in red can be looked upon as if it were a crude model for Han's function in blue $= \exp(H/c.r)$ .
By the way, the volume of the "blue" universe can be calculated too, as actually has been done below.
That volume turns out to be approximately half the volume of the "red" universe.
Oops, that outcome is for the "blue" universe when limited to a radius of $(c/H)$ . For the whole VM uiverse we have a finite volume

$$ V = 4\pi\left[-e^{-\xi}(\xi^2+2\xi+2)\right]_0^\infty \left(\frac{c}{H}\right)^3 = 8\pi \left(\frac{c}{H}\right)^3 $$

which is $8/(4/3)=$ six times the volume of the "red" universe.
Or is it not the volume but only the mass that is finite?

[HanDeBruijn]

There are only fifteen numbered formulas in the whole paper. So it is not such a hard task to tabulate them. If we compare these formulas with similar ones in the previous Eggshell paper, then the following overview is obtained.

$$ \begin{matrix} {\bf \mbox{thread}} & {\bf \mbox{204}} & {\bf \mbox{thread}} & {\bf \mbox{256}} \\ T_z = T_0(1+z) & (1) & T_z = T_0(1+z) & (1) \\ u = \frac{U}{V} = \frac{4\sigma}{c} T^4 & (2) & u = \frac{U}{V} = \frac{4\sigma}{c} T^4 & (2) \\ P = \frac{1}{3}\frac{U}{V} = \frac{4\sigma}{3c} T^4 & (3) & P = \frac{1}{3}\frac{U}{V} = \frac{4\sigma}{3c} T^4 & (3) \\ n = r T^3 & (4) & n = r T^3 & (4) \\ L_\Lambda = -U H_0 & (5) & L_H = -U H_0 & (5) \\ F_\Lambda = \frac{Gm_1m_2H_0}{r^2c} & (6) & \mbox{check: is not a force} & \mbox{(X)} \\ U_{EU} = -\frac{G M^2}{R_U} & (7) & U = -\frac{G M^2}{R_U} & (6) \\ L_\Lambda = \frac{G M^2H_0}{R_U} = \frac{G M^2 c}{R_U^2} & (8) & L_H = \frac{G M^2H_0}{R_U} = \frac{G M^2 c}{R_U^2} & (7) \\ L_\Lambda = \frac{c^5}{4G} & (9) & L_H = \frac{c^5}{4G} & (8) \\ F_\Lambda = \frac{c^5}{4G} & (10) & F = \frac{c^5}{4G} & (9) \\ F_g = -\frac{G M^2}{R_U^2} & (11) & F_g = -\frac{G M^2}{R_U^2} & (10) \\ T_{shell} = \left(\frac{L_H}{4\pi R_U^2 \sigma}\right)^{1/4} & (12) & T_{shell} = \left(\frac{L_H}{4\pi R_U^2 \sigma}\right)^{1/4} & (11) \\ u_g = \left(\frac{3c^2H_0^2}{16\pi G}\right)^{1/4} & (13) & u_g = \left(\frac{3c^2H_0^2}{16\pi G}\right)^{1/4} & (12) \\ H_{bh} = \frac{c}{R_S} & (19) & H_{bh} = \frac{c}{R_S} & (13) \\ \rho_{bh} = \frac{3c^2}{8\pi G R_S^2} & (20) & \rho_{bh} = \frac{3c^2}{8\pi G R_S^2} & (14) \\ \rho_{bh} = \frac{3H_{bh}^2}{8\pi G} & (21) & \rho_{bh} = \frac{3H_{bh}^2}{8\pi G} & (15) \end{matrix} $$

I may be blind, but in my view hardly any progress can be noticed, at least not in the mathematics. I would have expected quite different math for the thick shell universe as compared with the thin (egg)shell universe.

[ExpEarth]

@HanDeBruijn I would have expected quite different math for the thick shell universe as compared with the thin (egg)shell universe.

Bingo! You're quite right that one would expect a lot of math to move from the thin-shell to thick-shell models. To do that properly would have required a deep dive into the Einstein field equations of liquid or gas spherical masses, something that I would have to seriously retool for. The extensions of the Ni-Neslusan-deLyra solutions to an actual thick-shell universe still need to be done! The future problem is that those who may attempt this will be tempted to do it in the expanding universe model. This will lead to an unrecognizable universe, I'm afraid. So my approach was to use Gupta's idea of a hybrid model and use my eggshell model as an extreme version of the Ni shell model. The math in the eggshell model is a lot simpler. I called it a toy model. The idea is that the features of this toy model can then be blended with LCDM model features in different combinations to attain suitable results. This is why the math is all the same. Of course the LCDM contribution would be small or nonexistent, but by expressing it this way it became possible to communicate my findings to very skeptical reviewers. There were only one or two reviewers over many journals who were intrigued with my original eggshell model (hmmm, similar as here in ACG!)

[HanDeBruijn]

The true physical volume of the interior space is thus smaller than its apparent coordinate volume

Read The volume of sphere using integrals, skip to halfway the derivation and proceed for the apparent coordinate volume of a mass $M$ with density $\rho=\rho_0$ and radius $R_U = c/H$ :

$$ M = \int_0^{R_U} \rho \mbox{ } 4\pi r^2 dr = \rho_0 \frac{4}{3}\pi R_U^3 = \rho_0 . \frac{4}{3} . \pi \left(\frac{c}{H}\right)^3 = \rho_0 \times \mbox{(apparent coordinate volume)} $$

The above statement by @ExpEarth turns out to be true. Let's see how the Variable Mass Theory deals with it. In that case the mass density is given instead by $\rho = \rho_0 e^{-H/c.r}$ . Now proceed analogously as with the "normal" spherical mass.

$$ M = \int_0^{R_U }\rho\mbox{ } 4\pi r^2 dr = \rho_0 \int_0^{c/H} e^{-H/c.r}\mbox{ } 4\pi r^2 dr = \rho_0 \times \mbox{(true physical volume)} $$

We are using the dimensionless

$$ \int e^{-\xi}\xi^2 d\xi = -e^{-\xi}(\xi^2+2\xi+2) \quad \mbox{with} \quad \xi = H/c.r \quad \mbox{and} \quad 0 \le r \le c/H $$

resulting in

$$ M = \rho_0 4\pi\left[-e^{-\xi}(\xi^2+2\xi+2)\right]_0^1 \left(\frac{c}{H}\right)^3 = \rho_0 . 4(2-5/e) . \pi \left(\frac{c}{H}\right)^3 $$

where $(2-5/e) \approx 0.160602794$ and so $(2-5/e) \lt 1/3$ : (true physical volume) < (apparent coordinate volume) .
Quod Erat Demonstrandum (QED).

It is even noticed that $0.160602794 \lt 0.166666666 = 0.333333333/2$ , ipse est (i.e.) less than one half !

[Francois-Zinserling]

Dear Matthew
@ExpEarth

Congratulations on having your article published. I have not been able to follow up on all the references. There is a mountain of it!

I would however like to revisit some of our earlier (email) discussions here with the hope of provoking some further discussion. My initial skepticism to the 'black hole universe' is somewhat allayed, although I still don't see us, here, as being similar to what is in a black hole, over there. :) You are likely to find more resistance to that thinking.
I'm also not on board with the filaments that bind all particles, since the possible permutations between all particles of mass (and you must definitely add another filament between each particle of charge) must certainly break the computer that runs this universe.

I did notice your referral again to Annila's 'photon-pair vacuum'.
First question. Do you think Annila coined this term, or have you come across earlier references?

For a moment let's replace Fatio and Le Sage's 'corpuscles' with Annila's photon pairs ...

Then I would like to paint a picture mostly for the benefit of others:
Let's say (hypothetically) that all quasars convert mass to energy and spew energy out as paired photons. Being paired and out-of-phase, these photons can comfortably escape black holes and/or quasars since the photon pair is only left with spin=2 quantum property, but no net E or B field components to hold them back. Now also picture the quasars as slow-motion firehoses that broke loose; thus the photon pairs are not just being jetted in 'one' direction from any quasar but on a cosmic timescale they are sprayed all over the place. /end picture.

1. Now place yourself at the centre of your proposed shell universe and combine with the above scenario: In any direction you look, there will be at some distance quasars sending photon pairs at you. This will make it appear as if you are in the centre of the universe because photon pairs are coming from all directions. Those that reach you remain unchanged since they had no particle interaction. But it will appear this way no matter where you are in the universe, you will always think you are in the centre. Any relative movement you might have, or maybe a non-homogenous quasar density in some direction, will make it appear as if you are not in the centre, but you will still appear to be 'close' to the centre unless you could maybe achieve v~c at which things will appear markedly skewed.
2. Let's say again hypothetically that these photon pairs interact with matter and are thereby depleted, through mechanisms of e.g. gravity and/or electric fields. In any direction you look, it would appear if there are more photons at a distant location, since all photons aimed directly at you must necessarily be depleted over distance, so the intensity aimed directly at you is gradually waning over vast distances. Is this not exactly Hubble? It means though you will still measure H no matter where you place yourself, even so it has to be 2.7K 'at our edge' of the universe. An analogy might be the light coming off an infinitely large wall. No 1/r^2 or even 1/r weakening of intensity. Of course, this also means expansion is not required.
3. Last one. Again, if you look into the distant 'as far as you can see' distance, the remaining 'outside' universe must appear to be a solid shell, even if it is not. Somewhat along the principle of Olber's Paradox, except in this case the effect of the distant universe is very 'visible' and has the appearance similar to that of a solid wall. Because from wherever you look in any direction, eventually you must see a solid object.

[ExpEarth]

Thanks Francois @Francois-Zinserling ! I think our models or model styles are very similar. Your comments helped me to think about how gravity works with the paired-photon model. I didn't really talk about gravity much in the paper, as there was already too much for reviewers/readers to digest.

Let's go over your points. The way you describe things is similar to what I would have said prior to the point I made the universe into a black hole universe. Of course the idea that the universe and black holes have similar structures seems fantastical, but once you appreciate the functions they do it all becomes straightforward. The black hole structure in all cases locks in matter and radiation, apart from jets, inside the structures. They thus become semi-autonomous entities, doing their own metabolic thing. Without this sequestering, the universe and black holes would not be able to do the things they do. Most important is the CMB cycle (Figure 3).

It's important to recognize that in rotating black holes, a spherical shell would likely become unstable. It would collapse to a toroid-like structure, similar to the dark energy star model. The photos of the supermassive black holes in our galaxy and Andromeda - looking like The One Ring - suggest this is what happened.

The picture I have is slightly different from Arto Annila's. He calls it the "paired-photon vacuum" (Fig. 2). For many years I had suggested that particles must be linked by photonic filaments. I thought the photonic elements might be similar to virtual photons. The reason why it has to be photonic filaments relates to gravity and the Hubble luminosity. The Hubble luminosity L = UH is central (Fig. 4). It seems to hold in all cases where other energy sources do not dominate. No one has shown me I'm wrong about it, after almost two decades. It is simply the easiest way I can image how gravitational potential energy degrades to photons - to have all masses connected by these fine filaments of photons whose energy matches U . Now you argue that interconnecting all the universe's particles this way is unimaginably complex, but keep in mind that photons have ways of interacting to reduce this complexity. Think of each particle as being like the heart of a circulatory system. The tiny photonic 'vessels' all eventually converge into large flows entering and leaving the particles. The particles themselves are photonic in nature. This is what Arto Annila preaches: everything is made of photons. I term the paired-photon filaments as spacetime, for simplicity. I don't think Arto is yet saying the filaments are linked directly to particles as I do.

So the shell structure allows CMB photons to be locked inside, giving rise to a cycle. The hottest at are in the shell, the coolest near us. The shell is at the same time supported by the Hubble luminosity, which acts as a cosmological constant.

Your points 1-3, hey I was there, except that I would not limit the photon-pair emission to quasars. The photon filaments emerge from and reenter all particles. What you say about an effective wall that seems to exist, with us at the centre, is what I thought too, before. Here's the problem though. Supposing we are not at the centre of a real shell, but rather a pseudo-shell, it becomes hard to explain the CMB temperature structure. Are you saying that the CMB temperature would be higher in the pseudo-shell region? Then, since our location is not special, there should be a matching region of hotter CMB at our position, radiation that must cool to form a cooler CMB at the pseudo-shell. But where is the local hot CMB? And did we not just say the pseudo-shell has a hotter rather than cooler CMB? It becomes impossible to fix. And the measurements of CMB temperature suggest that the actual temperatures of the CMB do increase with distance (though many/most in ACG continue to question this). The pattern of CMB temperatures point to a real shell, not a pseudo-shell.

To all: as long as one holds on to the idea that the CMB is 2.7 K everywhere, the advantages of the shell structure can't be appreciated. I would suggest that everyone try to read up on the papers making those measurements and try to debunk them.

Now getting back to gravity, the paired-photon model leads to a simple mechanism. Looking at Fig. 2, you can see that where filaments have unpaired (real) photons, the filaments are extended slightly. Where the photons are paired up, the filaments are more compact. What I suggest is that when photon energy undergoes the Hubble redshift, a portion of the photon pairs up with a portion of a photon moving the other way. This allows the filament to shorten. And since the filament is connected to particles, those particles will be drawn together in gravity. My optical gravity model of a few years ago is not enough. We need absorption of photon energy. The CMB is driving gravity.

[HanDeBruijn]

[ExpEarth]

On that front, the key points in my paper, concerning the Ni shell structure, the Hubble luminosity, the CMB temperature distribution, etc., are all scientifically testable.

[HanDeBruijn]

Something for you, @ExpEarth ?
Nested solutions of gravitational condensate stars :

[ExpEarth]

Thanks, Han. The idea of nested shells could be relevant. The gravitational condensate star, or gravastar, is quite a speculative notion, however. It's one of the alternative solutions that have been proposed for black holes. They have an exterior shell, usually thin (but in this paper thin or thick) and the shell is supported by a hypothetical entity called a Bose-Einstein condensate. That's the problem with the alternate models. They all rely on special assumptions. That's where the Ni-Neslusan-deLyra solutions are different. They are based on ordinary baryonic matter exclusively. They are new solutions in GR just found recently.

[ExpEarth]

I did a little news article for Science X Dialogs on my model. It could help simplify things for some:

https://phys.org/news/2024-09-shell-universe.html

[genotics]

This is quite an achievement Matt, and I'm glad you're still developing your cosmological model. What I find fascinating is the resemblance to a nested torus vortex electron model I am developing. Of course it is not my idea, as Adolphe proposed it in his papers. I am merely attempting to link it properly to the empirical data and other proposals, such as Malcolm's relativistically spinning sphere. Soon you will have to dive into fluid dynamics and we will meet at the bottom of the pool.

[ExpEarth]

Thanks Roy. I hope you don't find me in the fluid mechanics pool, though, as I would likely need to be resuscitated!

On the electron structure, your brief description reminds me of Arto Annila's model. He thinks that everything is made ultimately of photons, including the vacuum (or spacetime). You might want to check his video chapter from his book Back to Reality https://www.youtube.com/watch?v=9SPKrfWMsM0 The part on the electron starts around the 23 minute mark, but the whole video is interesting.

[ExpEarth]

Seems like Sabine didn't like my model! She looked at some parts of it, but missed the main points on how the universe actually functions. She goes nuts!
https://www.youtube.com/watch?v=bwOERPO7xT4&t=85s

[Francois-Zinserling]

10 points for getting on Sabine's radar, minus some few many lots of points for getting your ideas shredded!
Or maybe any publicity is good publicity?
How did you manage to get it on her desk?

[ExpEarth]

Thanks, Francois. I didn't send it to her. Someone must have brought it to her attention or maybe she saw my short piece on it in phys.org. While I had hoped she would do a video on my paper, obviously the result was not what I had hoped for! Quite a shock actually. I can't say whether the net result is bad or good for my theory. I know a lot more people have looked at my paper now.

The strange thing is she never actually got to the main parts of my theory. She didn't even make it past the introduction. She got stuck on the point about why we don't see a blueshift in photons from stars closer to the centre than we are. The whole paper dealt with that! I'm thinking of doing a video response to it in Youtube, but would enough people see it?

[HanDeBruijn]

she never actually got to the main parts of my theory.

No, because Sabine - just like me - does not know where to find those main parts.

we don't see a blueshift in photons from stars closer to the centre than we are.

Of course not. Because there is NO closer to the centre than we are.

I'm thinking of doing a video response to it in Youtube

Take my advice, Matt: don't make it worse than it already is.

would enough people see it?

Is being (in)famous the only thing you care about?

[RedshiftDrift]

"It's unstable" is what ruins everything. Unstable things need another explanation to happen, so the new model augmented with another explanation is already too many epicycles.
https://www.youtube.com/watch?v=bwOERPO7xT4&t=236s

Negative point mass, really? Photonic space-time? The problem with contemporary cosmology is that too many epicycles are used to make it work. This is the main criticism used by the "Cosmology Group". Why propose a solution that's just as bad?

I'm surprised, but impressed, that Sabine spent three hours trying to understand the paper, she is very thorough!

[ExpEarth]

Too many epicycles?? Give me a break!! You say she was thorough and she was indeed thorough when she looked at and discussed the papers on the Ni solutions. But even on those she was wrong. DeLyra never said anything about a point negative mass. That was her concoction. I introduced the Ni solutions as a way to solve the cosmological 'tensions', but then pointed out that there was an issue that needed to be resolved for that to work. This was completely normal science. Once she saw my mention of photonics spacetime she just stopped. She didn't get to the main ideas of my paper at all! Thorough you say??

From the general relativity side, the Ni solutions alone would give black holes and the shell universe stability. But on the quantum gravity side there is stability also. It all relates to the Hubble luminosity, which I have described here many times. The repulsive forces generated by the Hubble luminosity inside a shell black hole exactly balance the inward gravitational forces. Sabine never got to the sections on the black hole universe, black holes or the Hubble luminosity at all! She totally missed my model.