OSP Journal of Physics and Astronomy

The beautiful Titius-Bode law about Solar planetary orbits discovered in 1766, is considered that it is a mathematical coincidence rather than an "exact" law, because it has not yet been physically proved. However, if the disturbance restoration and the stability of the asteroid belt orbit are considered, there must be some underlying logical necessity.

Gravitomagnetic tensor is derived from General Relativity comparing the action for a continuous distribution of matter and the action for the electromagnetic field.

Similarly  to  the  spin–orbit  interaction  there  is  a  magnetic  field  acting  on  the  star  S2  induced  by  the  supermassive  black  hole  gravitational field.   The gravitational magnetic force is derived from Special Relativity force transformations.  Energy associated with this new force is stored in the dark matter energy tensor D (4, 0) related to the Riemann curvature.

Dark matter gravity is generated by D(4,0) energy related directly to the  S(4,0)  tensor,  however  this  gravity  is  attributed  to  exotic  particles never detected, galaxies in our universe are rotating with such speed that the gravity generated by their observable matter could not possibly hold them together.

Total  Energy  T(4,0)  and  energy  tensors  are  defined  to  complete  the General  Relativity  field  equations.   The  Ricci  decomposition  is  a  way  of breaking up the Riemann curvature tensor into three orthogonal tensors, Z(4,0), Weyl tensor C(4,0) and S(4,0).

In the Eigen Theory of the physical world, the fundamental form of a particle of matter is a distribution of points that forms a manifold of its own. Each point results from the intersection of a corresponding pair of eigenvelocity vectors, which are functions of a pair of symmetric and antisymmetric tensors characteristic of gravitation and electromagnetism respectively. The theory develops in three stages. The first and second stages produce the wave and particle aspects matter. The third stage formulates the base manifold, characterised by an eigenfield of a second pair of symmetric and antisymmetric tensors, in which the particle moves as a whole whilst rotating about an axis through the particle centre. The first two stages expose the reality behind matter-antimatter, the quantum mechanical wave-particle duality and the results of the double-slit experiment. The third stage reveals the nature of dark energy and the structure of dark matter. In Eigen Theory Quantum Mechanics becomes restructured; in particular the uncertainty principle ceases to exist.

Poynting vector, Maxwell stress tensor and Lorentz force are generalized in curved space derived from gravitomagnetic tensor.

Gravitomagnetic tensor is derived from General Relativity comparing the action for a continuous distribution of matter and the action for the electromagnetic field.

Gravitational magnetic force is also derived from Special Relativity force transformations. Similarly to the spin-orbit interaction there is magnetic field acting on the star S2 induced by the supermassive black hole gravitational field.

Energy tensors are defined to complete the General Relativity field equations. Ricci decomposition is a way of breaking up the Riemann curvature tensor into three orthogonal tensors, Z, Weyl tensor C and S.

In a manifold with a linear connection if the torsion tensor vanishes then the Christoffel symbols are symmetric in the lower indices, this is the motivation to call it the symmetric connection.

The requirement of being metric, the length is preserved by parallel transport and symmetric leads to the unique result for the Christoffel symbols of the connection.

This distinguished linear connection on a Riemannian manifold is usually called the Riemann connection or the Levi-Civita connection.

We consider a connection which is metric but not symmetric, the torsion tensor does not vanish and we study the conservation laws depending on it, the non-symmetric Ricci tensor and the action.

As light travels extreme distances through space, its frequency slowly diminishes (attenuates). We observe this phenomenon as a redshift, the tendency of visible light to drop toward the red end of the spectrum. This study explains the true nature of redshift and provides a formula for estimating the rate at which light attenuates over extreme distances. When redshift is properly understood, it can tell us how far light travels before it drops beneath the visible spectrum.

As light travels extreme distances through space, its frequency slowly diminishes (attenuates). We observe this phenomenon as a redshift, the tendency of visible light to drop toward the red end of the spectrum. Unfortunately, for over 100 years redshift has been misinterpreted as a Doppler effect. This is the fundamental cosmological error that creates the fatal flaw in these misconceived hypotheses: big bang theory, expansion theory, Hubble’s law, dark matter, and dark energy. This study explains the true nature of redshift and provides a formula for estimating the rate at which light attenuates over extreme distances. When redshift is properly understood, it can tell us how far light travels before it drops beneath the visible spectrum.

The gravitational magnetic force is derived from Special Relativity force transformations. Energy associated with this new force is stored in the dark matter energy tensor D (4, 0) related to the Riemann curvature.

Dark matter gravity is generated by D(4,0) energy related directly to the S(4,0) tensor, however this gravity is attributed to exotic particles never detected, galaxies in our universe are rotating with such speed that the gravity generated by their observable matter could not possibly hold them together.

Total Energy T (4, 0) and energy tensors are denied to complete the General Relativity field equations. The Ricci decomposition is a way of breaking up the Riemann curvature tensor into three orthogonal tensors, Z (4, 0), Weyl tensor C (4, 0) and S (4, 0).

Similarly to the spin-orbit interaction there is a magnetic field act-ing on the star S2 induced by the supermassive black hole gravitational field. The gravitational magnetic force is derived from Special Relativity force transformations. Energy associated with this new force is stored in the dark matter energy tensor D (4, 0) related to the Riemann curvature.

Dark matter gravity is generated by D (4, 0) energy related directly to the S (4, 0) tensor, however this gravity is attributed to exotic particles never detected, galaxies in our universe are rotating with such speed that the gravity generated by their observable matter could not possibly hold them together.

Total Energy T (4, 0) and energy tensors are denied to complete the General Relativity field equations. The Ricci decomposition is a way of breaking up the Riemann curvature tensor into three orthogonal tensors, Z (4, 0), Weyl tensor C (4, 0) and S (4, 0).

In 1982, MIT physicist Frank Wilczek predicted and named ANYONS, quasiparticles (particle-like formations) that are confined to 2 dimensions and were discovered in 2020. The name might come from Prof. Wilczek's lighthearted comment "anything goes". This article's main goal is to show that anyons could be another name for 1) virtual particles, 2) Mobius strips, and 3) figure-8 Klein bottles. Along the way, we'll see the picture painted by the article confirm that Einstein's dream of gravitational-electromagnetic unity fits in with anyons being Mobius strips. The topological hypothesis offers an explanation of dark matter and dark energy. We'll also have encounters with intergalactic travel and imaginary computers. They really could exist but are imaginary in the sense that they use imaginary time (as well as space-time warping).

This hypothesis is the result of my conviction that science will one day prove everything in space and time is part of unification.  In "a Brief History of Time", Stephen Hawking wrote,"If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution (of the universe's puzzles) by investigating parts of the problem (such as general relativity and quantum mechanics) in isolation."

The goal: to establish a “proof of concept” to which equations can be added. It’s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-3 Klein bottles and Wick rotation works better. The failed cosmologies have impressive points leading to the idea that they’re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but it’s supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter, dark energy, and electromagnetic-gravitational union.  Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.