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On the Fractal Structure of Space-Time

Martinez A

We show that strings are not one-dimensional objects and that they can be continously stretched to become 2-branes. This in turn suggests that strings have fractal structure. We then proceed to analyze curvature variations inside black holes, which after making use of their entropy properties and applying them a classical theorem in Riemannian Geometry, leads us to conclude that space-time is indistinguishable from energy. By considering the string’s structure mentioned above, this implies that space-time itself has fractal structure. Applications of such results include a solution of the problem regarding the universe’s shape by defining it as finite in size and with zero global curvature, and an explanation of high-temperature superconductivity by means of 2-branes’ stickiness property.