Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves

TL;DR

This paper proposes that considering retardation effects from the Lorentz symmetry in general relativity can explain galactic rotation curves without dark matter, challenging conventional models that neglect these effects.

Contribution

It introduces a novel approach by incorporating retardation effects from GR's Lorentz symmetry to explain galactic rotation velocities without dark matter.

Findings

Retardation effects significantly influence galactic rotation models.

Galactic velocity profiles can be explained without dark matter.

The approach challenges traditional Newtonian and dark matter paradigms.

Abstract

The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted as the Lorentz group of symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter.