Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field — the Lanczos tensor field — that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.

Lanczos potential of Weyl field: interpretations and applications

An attempt is made to uncover the physical meaning and significance of the obscure Lanczos tensor field which is regarded as a potential of the Weyl field. Despite being a fundamental building block of any metric theory of gravity, the Lanczos tensor has not been paid proper attention as it deserves. By providing an elucidation on this tensor field through its derivation in some particularly chosen spacetimes, we try to find its adequate interpretation. Though the Lanczos field is traditionally introduced as a gravitational analogue of the electromagnetic 4-potential field, the performed study unearths its another feature – a relativistic analogue of the Newtonian gravitational force field. A new domain of applicability of the Lanczos tensor is introduced which corroborates this new feature of the tensor.

Non-inertial effects on generalized KG-oscillator in the presence of Coulomb-type potential in topological defects geometry

In this work, we solve a generalized KG-oscillator subject to a scalar and vector potential of Coulomb-types under the effects of a uniform rotation in cosmic string space-time. We obtain the energy eigenvalue and eigenfunction, and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states. We see that the presence of potential allow the formation of bound states solution and the energy level and wave-function for each radial mode depend on the global parameters of the space-time.

Generalized KG-oscillator with a uniform magnetic field under the influence of Coulomb-type potentials in cosmic string space-time and Aharonov-Bohm effect

We solve a generalized Klein-Gordon oscillator (KGO) in the presence of a uniform magnetic field including quantum flux under the effects of a scalar and vector potentials of Coulomb-types in the static cosmic string space-time. We obtain the energy and corresponding eigenfunctions, and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

Klein–Gordon oscillator subject to a Cornell-type potential in the rotating cosmic string space-time and Aharonov–Bohm effect

Klein–Gordon oscillator in the background space-time generated by a rotating cosmic string subject to a Cornell-type scalar and Coulomb-type vector potentials including an internal magnetic flux is studied. We obtain the relativistic energy eigenvalues and the corresponding eigenfunctions and analyze a relativistic analogue of the Aharonov–Bohm effect for bound states.

Effects of Kaluza-Klein Theory and Potential on a Generalized Klein-Gordon Oscillator in the Cosmic String Space-Time

In this paper, we solve a generalized Klein-Gordon oscillator in the cosmic string space-time with a scalar potential of Cornell-type within the Kaluza-Klein theory and obtain the relativistic energy eigenvalues and eigenfunctions. We extend this analysis by replacing the Cornell-type with Coulomb-type potential in the magnetic cosmic string space-time and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

Quantum influence of magnetic flux on spin-0 scalar charged particles in the presence of external field in a spinning cosmic string space-time

In this work, we investigate spin-0 massive charged particles in the background space-time induced by a spinning cosmic string coupled to a homogeneous external magnetic field parallel to the string including a magnetic quantum flux. We compute the energy eigenvalues and eigenfunctions and analyze a relativistic analogue of the Aharonov-Bohm effect.

Quantum Influence of Topological Defects on a Relativistic Scalar Particle with Cornell-Type Potential in Cosmic String Space-Time with a Spacelike Dislocation

We study the relativistic quantum of scalar particles in the cosmic string space-time with a screw dislocation (torsion) subject to a uniform magnetic field including the magnetic quantum flux in the presence of potential. We solve the Klein-Gordon equation with a Cornell-type scalar potential in the considered framework and obtain the energy eigenvalues and eigenfunctions and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

Seesaw mechanism and pseudo C-symmetry

It is shown that the specific “charge conjugation” transformation used to define the Majorana fermions in the conventional seesaw mechanism, namely $$(\nu _{R})^{C}=C\overline{\nu _{R}}^{T}$$(νR)C=CνR¯T for a chiral fermion $$\nu _{R}$$νR (and similarly for $$\nu _{L}$$νL), is a hidden symmetry associated with CP symmetry, and thus it formally holds independently of the P- and C-violating terms in the CP invariant Lagrangian and it is in principle applicable to charged leptons and quarks as well. This hidden symmetry, however, is not supported by a consistent unitary operator and thus it leads to mathematical (operatorial) ambiguities. When carefully examined, it also fails as a classical transformation law in a Lorentz invariant field theory. To distinguish it from the standard charge conjugation symmetry, we suggest for it the name of pseudo C-symmetry. The pseudo C-symmetry is effective to identify Majorana neutrinos analogously to the classical Majorana condition. The analysis of CP breaking in weak interactions is performed using the conventional CP transformation, which is defined independently of the pseudo C-transformation, in the seesaw model after mass diagonalization. A way to ensure an operatorially consistent formulation of C-conjugation is to formulate the seesaw scheme by invoking a relativistic analogue of the Bogoliubov transformation.