Let me declare the mechanics of the Black Eye model. I will not discuss vents or spouts; these are minor aspects. Let's not get hung up on them.
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First the setup: We must recognize that galaxies move through space collectively in a singular direction and that this is the fastest speed this matter is moving in.
All matter in our Milky Way is moving at their fastest speed away from the original catapulting action of the materialization process, some 13.8 billion years ago, a speed that is on-going.
The most important aspect to note is that this action is not based on gravity. Please let this reality sink in.
When discussing Black Hole/Black Eye models, we must recognize this speed among the material outcome: the fastest speed in one single direction for the entire collective of matter is the first part to understand about the basics.
Only then can we review gravity as part of this outcome.
In the circular spin of the Milky Way, we have the interplay of matter being pushed out because of the spin, while matter is being pulled together by gravity. An interplay for sure.
Let's ignore all the smaller spins such as seen with the Solar System and focus on just the larger spin of the Milky Way.
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In the Black Eye model, all masses in the galaxy have their own gravity, and collectively we find the following:
All are pulling on all (in as far as gravity reaches, which is a different discussion), and this delivers a net-zero outcome in the exact center.
Note once more how net-zero is not the same as zero. In the entire galaxy (in as far as gravity reaches) we have the same amount of gravity, yet the internal tension is distinctive. Allow me the word tension here to declare gravity in a different manner.
Along the outer edges of a galaxy, we have the stronger inward tension. The pull is toward the center.
Half-way toward the center, the pull is still toward the center, yet there are pulls in other directions as well. The tension we find in that location is therefore diverse, with the pull toward the center winning out.
In the center, we find the net-zero spot, meaning that the tension is most diverse, optimized in such a manner that no specific direction wins out. In effect, the entire set of matter in a galaxy is pulling equally strong on this center spot.
The part to understand occurs exactly next to the net-zero spot. The location where we find the perfect balance is accompanied by the strongest outburst toward one side of the galaxy.
You dislike analogies, but you do understand the Eye of the Storm, indicating that the center is a net-zero wind force location, while the Wall of the Eye is the most extreme expression of wind force on planet Earth. We find net-zero in the middle and the greatest extreme right next to it.
The analogy of the Eye of the Storm shows collective aspects, though not like individual masses as seen in a galaxy. It is an imperfect analogy, but it does show well the surprising maximum sitting right next to the minimum in the center.
In the center of planet Earth, we actually witness the same outcome, too, of a maximum sitting around a minimum of some kind. The inner core is two parts: the center inner core is solid while the immediate inner core surrounding the center is fluid. Their chemical reality is near the same. It is the net-zero quality of the center that makes this matter be solid. It is the first opportunity for friction that churns that matter around the center into a fluid (and heats up the planet).
There are more analogies to consider, but knowing how bad you are at analogies I will stop here. The point I am trying to show is how the net-zero spot is a minimum of some kind of tension, and how the immediate surrounding contains the max of release of tension in specifics.
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When a single mass is attracted by the collective center in a galaxy (in other words, does no longer follow the initial setup of the larger spin of the galaxy and the specific spin in which it was existing), then that mass will likely not fall into the Black Eye. Rather, it will get swung around the Black Eye.
This is similar to a bird getting caught in the Wall of the Eye of the Storm and being pulled into the vortex of the Wall, circling parts therefore with the Wall, being spit out at some point.
On Earth, there will be external aspects that influence the outcome. In space, we do not have those. The entire gravitational field is established by all these masses.
Lastly, I will again point to Journey to the Center of the Earth, how compasses moved wildly once the Lidenbrock team had reached the very center. Jules Verne wrote a good novel (part fantasy, part science).
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Synergy is an additional outcome while there are no new parts added to the mix.
The Black Eye synergy is therefore the Great Depression in the center of a galaxy, created by all masses in a galaxy, and this established its own specific environment, fully based on gravity. A new environment got established while nothing was added; all ingredients were there already.
Contrast this with the Black Hole model in which the specific environment is explained by a single material center, and you can see how both models provide the exact same outcomes but each from a different perspective: singular in the material center for the Black Hole model, or collective in surrounding a non-material center for the Black Eye model.