Abstract
In this work, we present our theory and principles of the mathematical foundations of Lobachevskian (hyperbolic) astrophysics and cosmology which follow from a mathematical interpretation of experimental data in a Lobachevskian non-expanding Universe. Several new scientific formulas of practical significance for astrophysics, astronomy, and cosmology are presented. A new method of calculating (from experimental data) the curvature of a Lobachevskian Universe is given, resulting in an estimated curvature-K on the order of 10−52 m−2. Our model also estimates the radius of the non-expanding Lobachevskian Universe in a Poincare ball model as approximately 14.9 bly. A rigorous theoretical explanation in terms of the fixed Lobachevskian geometry of a non-expanding Universe is provided for experimental data acquired in the Supernova Project, showing an excellent agreement between experimental data and our theoretical formulas. We present new geometric equations relating brightness dimming and redshift, and employ them to fully explain the erroneous reasoning and erroneous conclusions of Perlmutter, Schmidt, Riess and the 2011 Nobel Prize Committee regarding “accelerated expansion” of the Universe. We demonstrate that experimental data acquired in deep space astrophysics when interpreted in terms of Euclidean geometry will result in illusions of space expansion: an illusion of “linear space expansion”—Hubble, and an illusion of “accelerated (non-linear) space expansion”—Perlmutter, Schmidt, Riess.
Highlights
We present our theory and principles of the mathematical foundations of Lobachevskian astrophysics and cosmology which follow from a mathematical interpretation of experimental data in a Lobachevskian non-expanding Universe
In a series of our work on applications of Lobachevskian geometry to physics, astrophysics, and cosmology [7]-[12], we proved that a non-expanding Lobachevskian Universe, being a Lorentz invariant entity, is able to explain in a coherent, Lorentz invariant way, all electromagnetic observable phenomena, including cosmological redshift, Doppler shifts, non-Euclidean intensity fading, space caused aberration, velocity caused aberration, polarization of light rotation, and CMB
The content of this paper can be regarded as physical Lobachevskian geometry, which is a “translation” of statements and formulas of Lobachevskian geometry into the language of physics
Summary
The motivation for the present paper is to give a rational, in terms of clearly defined mathematics, explanations of some deep space astrophysical data. The aim of the present work is twofold: 1) To give a rigorous mathematical analysis of data acquired in deep space astronomy and astrophysics. In a series of our work on applications of Lobachevskian geometry to physics, astrophysics, and cosmology [7]-[12], (see Kadomtsev [13]), we proved that a non-expanding Lobachevskian Universe, being a Lorentz invariant entity, is able to explain in a coherent, Lorentz invariant way, all electromagnetic observable phenomena, including cosmological redshift, Doppler shifts, non-Euclidean intensity fading, space caused aberration, velocity caused aberration, polarization of light rotation, and CMB. Our exposition is done exclusively within the framework of Lobachevskian geometry and Maxwellian electromagnetics, which both are clearly defined and well understood
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