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 theory presented in this website.

As a starting point, the anatomy of the Schwarzschild black hole (SBH) is compared to the anatomy of M_Set. All of the main features of the SBH, including the singularity, the event horizon, the lesser known photon sphere and the black hole itself, are mapped to features of the M-Set geometry. The concepts of time, space-time curvature and black hole entropy are also addressed. 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? 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 hole does lead to some interesting predictions that differ from standard thinking. The evidence presented in this body of work should give pause to the idea of the black hole nature of M-Set and in general, to the intrinsic fractal nature of the universe.

Due to the controversial nature of this research, a few things need to be clarified. First of all, the circumstantial and highly speculative evidence presented in this body of work must be admitted. This idea was developed independently (by the myself) over many years of investigation, outside of the academic community. It began as a simple “thought experiment” and a few simple questions. What if relativity was never invented? What if the concept of fractal geometry predated relativity? Would we still have the concept of the black hole? Would we still be talking about event horizons and space-time curvature? This “thought experiment” is in no way meant to replace any of the currently accepted theories related to black black holes. Fractal geometry was not in the minds of the founders of the standard model of cosmology which is why it was not previously considered. This is a philosophically different approach to black holes and cosmology that looks nothing like the the way it was done before. That said, if it is possible that quasi-black holes exist in nature, then this research should not be ignored just because it is different.

Richard Feynman

Mandelbrot Set as a Quasi-Black Hole (click for paper)