Zero Gradient Gravity Fields, Dark Matter, and the Formation of Stars

We’ve mentioned in the past (to ourselves) that the formula for the Schwarzschild radius for a black hole, c2=2GM/rs tells us that no matter how thinly distributed a mass is, (such as 1 atom per cubic centimeter), if you have a large enough sphere of it, it will have a Schwarzschild radius when viewed from outside that volume. You can see this just by shuffling the equation around a little, so that c2/2G, which is a constant, equals M/r, the mass over the radius. For any given density, the mass, M increases with the cube of the radius, so for any given density, you can always find a radius that contains enough mass to equal the value c2/2G. Cute, huh?

I struggled for awhile wondering if an infinite 3D field of particles (which would appear to be flat gravitationally, that is, not have a gradient), would allow for overlapping apparent black hole horizons; everywhere you looked, there would be large, overlapping, spherical volumes that had enough mass to become black holes. Could this be our apparent cosmological horizon? But today (5/12/18) it occurred to me that the key feature of a black hole is that it has a gravitational gradient. You have to work to get out of the gravity well, or the idea of an event horizon is meaningless. But an infinite field of equally distributed mass has no gradient. It appears flat. Ergo, no event horizon, no matter the density.

Cruising along in deep space, there is, in essence, the same amount of mass pulling on you from all sides, that tenuous 1 atom per cm3. It could just as well be 10 atoms, or 100, or a million, with no noticeable effect. Once we attained a velocity, we would maintain that velocity – an object in motion remaining in motion. The interstellar gas would eventually slow you down, but it would take a very ong time.

Working with the 1 atom/cm3 extending to infinity, let’s say we superimpose another huge sphere of 1 atom/cm3 gas on top of that, so huge that it provides you with an event horizon (if I’ve done my math right, it would amount to roughly 1.5×105 light years in radius, or a ball 0.3 million light years in diameter). Now there is a mass and a very small gravity gradient. Is the event horizon based on the 2 atoms/cm3, or the 1 atom/cm3 density? We’ve already seen that the original 1 atom/cm3 field provides no gradient, so it would make sense that the only effect to the observer is to see the event horizon created by the new 1 atom/cm3 superimposed on the existing field; the other previously existing field is completely flat and cancels out.

However, the new field created by the new mass is going to affect both the old mass (1 atom of hydrogen per cm3 everywhere) and the new mass (1 atom per cm3 in the giant sphere). The object will form with twice the mass (in this case) predicted by the theory. When it’s first put in front of us, we will measure a mass represented by the 1 atom/cm3 in that volume. As it collapses and takes the background mass with it, it will finally produce a mass that accounts for the 2 atoms/cm3 that we actually started with. While it’s doing this, it will also be backfilling the area that it vacated with more interstellar gas, as that gas is also being pulled in by the gravity of the developing black hole, so the overall density of the universe will appear mostly unchanged, even around the black hole.

Practically speaking, this would be more likely to happen in a nebula, where the density is much higher.

One of the most interesting things about this process is that if there is an undetectable mass-type in the universe (like dark matter) that only interacts with regular matter through gravitation, and it’s distributed equally everywhere, then objects that form (planets, Suns, black holes) will also pull in this other mystery mass. As described above, the tenuous gas (1 particle per cc) that we currently measure may actually mass 2 or 10 or 100 particles per cc. We wouldn’t know since the field is flat. Since this new mass doesn’t react with normal matter, it will clump in the center of the object (although it may have its own chemistry and volume that prevent excessive density). Small objects existing on a larger mass (like humans), would have the dark matter pulled out of them, and when we performed tests like The Cavendish experiment to measure the gravitational constant, it would give us a good value for G for normal matter, and would give us erroneous results for the masses of the planets and the Sun. We would think the core is made of denser matter than it really is, both in the Sun and Earth. We know the mass of the Earth, but a substantial chunk could be dark matter and we’d never know it. Perhaps the iron core is made of silicon at half the molecular weight (which is interesting, because magma is 50% silicon dioxide, and only 9% ferrous oxide).

However, most objects that have formed in the last few million years are going to have some dark matter as part of their core. They have gravity, and any dark matter out there will be attracted to it just like regular matter, until an object forms which is part dark and light matter. This includes asteroids. Eventually, we’re going to move an asteroid, and when we do, the acceleration is going to leave the dark core behind. We may not notice it unless we’re looking for it, or if it’s a substantial enough part of the mass that we detect a mass-change in the object as it’s propelled. We would end up with two objects; the obvious light-matter asteroid, and the invisible dark-matter asteroid that could only be detected with a gravitational gradiometer. It would change the way we thought about the universe.

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