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SCIENTISTS ARE MODELERS. They devise mathematical models to explain what they perceive as reality. Pre-Copernicus, with human-centric and religious fervor, their model located Earth at their reality’s center. Newton refined the Copernican Solar System model by formulating cause and effect of its matter and energy. Einstein’s model combined energy and matter in his succinct mathematical relationship E = mc^{2}. He also posited a four-dimensional spacetime replacing the earlier three-dimensional perception.

In each case, and inherent in all science, experimental verifications gave confidence that the concept is well-rendered.

Which brings us to modern cosmology and the oddities of black holes, event horizons, and dark matter

**Black Holes and Event Horizons.** A black hole is a region of spacetime where gravity is so strong that nothing—neither particles nor electromagnetic radiation such as light—can escape it. A black hole’s event horizon is the edge of this puncture in the spacetime continuum.

**Dark Matter.** In studying galactic behavior, cosmologists in 1970 resolved discrepancies in predictions by positing the theoretical existence of dark matter: matter making up as much as 85 percent of the universe’s mass, yet being all but undetectable.

**The Planck Core Model.** In *space.com*, March 7, 2021, Paul Sutter writes of a possible new model in which “black holes could be stars with ‘Planck Hearts.’ ”

“According to a new study,” Sutter writes, “these black holes may instead be dark stars home to exotic physics at their core. This mysterious new physics may cause these dark stars to emit a strange type of radiation; that radiation could in turn explain all the mysterious dark matter in the universe, which tugs on everything but emits no light.”

How elegant this is! Just as Newton’s model clarified cause and effect, and Einstein’s linked matter and energy, this Planck Core model could resolve the puzzles of black holes and dark matter.

**Singularities**. Sutter observes, “Thanks to Einstein’s theory of general relativity, which describes how matter warps spacetime, we know that some massive stars can collapse in on themselves to such a degree that they just keep collapsing, shrinking down into an infinitely tiny point — a singularity.”

And yet, he notes, “The very property that defines a black hole—the singularity—seems to be physically impossible…. That means the current understanding of black holes will eventually need to be updated or replaced with something else that can explain what’s at the center of a black hole.”

**Enter the Planck Core.** Suppose that the matter at a black hole’s center resides in a “Planck Core,” compressed to the smallest possible scale, the Planck Length, 1.6 x 10^{-35} meters.

This modeling assumption, note, eliminates the apparent vagueness of an “infinitely tiny” point and the need for positing a singularity.

“With a Planck Core,” Sutter notes, “which wouldn’t be a singularity, a black hole would no longer host an event horizon…. But to outside observers, the gravitational pull would be so strong that it would look and act like an event horizon. Only extremely sensitive observations, which we do not yet have the technology for, would be able to tell the difference.”

**Dark Matter Explained?** What’s more, Sutter writes, “In a new paper, submitted Feb. 15 to preprint database arXiv, physicist Igor Nikitin at the Fraunhofer Institute for Scientific Algorithms and Computing in Germany takes the ‘radical singularity’ idea and kicks it up a notch. According to the paper, Planck Cores may emit particles (because there’s no event horizon, these black holes aren’t completely black). Those particles could be familiar or something new.”

Like, maybe, dark matter?

Sutter admits, “… the theory is barely more than a faint sketch of an outline, one without the physics or mathematics to confidently describe that kind of environment. In other words, Planck Cores are the physics equivalent of spitballing ideas.”

In his mathematics link, Elaine J. Horn writes, “According to one pure mathematician, pure mathematicians prove theorems, and applied mathematicians construct theories.”

My Ph.D. thesis is titled “Limit Points Which Are Not Sequentially Attainable.” It was a topological discussion in dynamical systems, admittedly pure. But, gee, do you suppose its mathematics might help describe behavior in approaching a Planck Core? ds

© Dennis Simanaitis, *SimanaitisSays.com*, 2021

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