Related papers: Thin-disk models in an Integrable Weyl-Dirac theor…
In this note we comment on a recent attempt by P. Burikham, T. Harko, K. Pimsamarn and S. Shahidi [Phys. Rev. D {\bf 107}, 064008 (2023)] to explain the galactic rotation curves as the result of the motion of time-like test particles in the…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
The approximately flat outer parts of spiral galaxy rotation curves are commonly interpreted as evidence for a discrepancy between the observed baryonic mass and the dynamical mass inferred from the measured orbital velocities. In many…
A short survey of some material related to conformal general relativity (CGR), integrable Weyl geometry, and Dirac-Weyl (DW) theory is given which suggests that CGR is essentially equivalent to DW with quantum mass equivalent to conformal…
Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply…
In this paper we study direct and inverse problems for discrete and continuous time skew-selfadjoint Dirac systems with rectangular (possibly non-square) pseudo-exponential potentials. For such a system the Weyl function is a strictly…
The dark matter hypothesis, which is not called into question here, explains why typical rotation curves of spiral galaxies do not follow a Keplerian profile. It is however not sufficient in itself to explain why the whole matter…
A modification of the Einstein-Hilbert Lagrangian by introducing a coupling between the Weyl tensor and the stress-energy tensor was proposed to explain flat galactic rotation curves without the exotic (non-baryonic) dark matter (DM) [1].…
In this paper, we consider homogeneous cosmological solutions in the context of the Weyl geometrical scalar-tensor theory. Firstly, we exhibit an anisotropic Kasner type solution taking advantage of some similarities between this theory and…
An exact but simple general relativistic model for the gravitational field of active galactic nuclei is constructed, based on the superposition in Weyl coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent matter…
The stability of general relativistic thin disks is investigated under a general first order perturbation of the energy momentum tensor. In particular, we consider temporal, radial and azimuthal "test matter" perturbations of the quantities…
We consider the recently introduced mimetic gravity, which is a Weyl-symmetric extension of the General Relativity and which can play a role of an imperfect fluid-like Dark Matter with a small sound speed. In this paper we discuss in…
We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenb\"{o}ck condition of the vanishing of the sum of the curvature and torsion scalar is also imposed. Moreover, a kinetic term for the torsion is also included…
The nature of spin current and the separation of charge current and spin current are two of the fundamental questions in spintronics. For this purpose the classical limit of the Maxwell-Dirac theory is investigated in the present…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are treated…
Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence…
Following our work from the previous paper about the study of effective Dirac algebra and the metric of the simple, special case of relativistic hydrogen atom, this paper gives the complete metric study defined by the effective Dirac…