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The Mandelbrot Set as a Quasi-Black Hole

Lori Anne Gardi
Year: 2017 Pages: 11

Black holes, originally described by general relativity, are of the most mysterious objects in the universe. Scientific consensus is that black holes do in fact exist in nature. Not only that, but they are considered as an important feature of our universe. The equally mysterious concept called fractal geometry, popularized by Benoit Mandelbrot, is also considered a very important feature of nature. Since fractals appear just about everywhere, it seemed reasonable to wonder if the geometry of the Mandelbrot set (M-Set) might also appear somewhere in nature. The main property that distinguishes fractal geometry from other geometries is the property of self-similarity. That said, it is well known that black holes come in many sizes. Stellar-mass black holes are typically in the range of 10 to 100 solar masses, while the super-massive black holes can be millions or billions of solar masses. The extreme scalability of black holes was the first clue that black holes may in fact have the property of self-similarity. This ultimately led to the quasi-black hole analogy presented in this essay. Here, the anatomy of the Schwarzschild black hole is used as a starting point for the analogy. All of the main features of black holes, including the singularity, the event horizon, the photon sphere and the black hole itself, are mapped to features of M-Set. Analogies for time, space-time curvature and black hole entropy are also presented. The purpose of this research is to see how far this analogy can be taken. Consensus is that both black holes and fractals exist in nature. Could there be a mathematical fractal that describes black holes, and if so, do they also exist in nature? Can this approach make a prediction and if so, is it testable? It turns out that M-Set as a quasi-black holes does lead to some interesting predictions that differ from standard thinking. Given the evidence presented herein, further investigation is suggested.