Abstract
The relatively high abundance of fractal properties of complex systems on Earth and in space is considered an argument in support of the general relativity of the geometric theory of gravity. The fractality may be called the fractal symmetry of physical interactions providing self-similarities of complex systems. Fractal symmetry is discrete. A class of geometric solutions of the general relativity equations for a complex scalar field is offered. This class allows analogy to spatial fractals in large-scale structures of the universe due to its invariance with respect to the discrete scale transformation of the interval d s ↔ q d s ˜ . The method of constructing such solutions is described. As an application, the treatment of spatial variations of the Hubble constant H 0 H S T (Riess et al., 2016) is considered. It is noted that the values H 0 H S T form an almost fractal set. It has been shown that: a) the variation H 0 H S T may be connected with the local gravitational perturbations of the space-time metrics in the vicinity of the galaxies containing Cepheids and supernovae selected for measurements; b) the value of the variation H 0 H S T can be a consequence of variations in the space-time metric on the outskirts of the local supercluster, and their self-similarity indicates the fractal distribution of matter in this region.
Highlights
For more than a hundred years, on 29 May 1919, the Eddington expedition made observations of a solar eclipse
It is proposed to consider the puzzle of fractals as a consequence of the properties of space-time and the symmetry of the interaction fields of matter
It is necessary to use the geometric theory of gravity, which is similar to general relativity (GR)
Summary
For more than a hundred years, on 29 May 1919, the Eddington expedition made observations of a solar eclipse. The main disadvantage of these modifications is that they introduce additional fundamental constants of gravitational interaction, which do not allow the use of the effects of the “dark sector” These parameters are defined from the same astrophysical observations of galaxies which need to be explained. 1/2 e ( it is called dilation) with transformation Φ ↔ σ Φ and the continuous conformal symmetry of space-time ds2 ↔ σ xk de s2 for the electron model This field should change the Newtonian gravitational interaction of all systems and its consequences would be self-similar properties of these systems. The description of the observed properties of matter by means of dynamic equations and symmetries of the interaction fields allows us to understand the nature of the universe at the micro and macro levels.
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