Effect of Motion of the Reference Frame on Geometrical Form of the Line of Monopole Singularity

TL;DR

This paper investigates how the geometrical shape of a monopole singularity line transforms under Lorentz transformations, revealing it becomes a hyperbola or retains its form depending on its position relative to the origin.

Contribution

It introduces a method using light signals to analyze the relativistic deformation of rigid lines and surfaces, specifically applying it to monopole singularity lines.

Findings

Line becomes a hyperbola when not passing through the origin in a moving frame.

Line retains its form if passing through the origin, modified by aberration.

Method based on light signals effectively tests geometrical form under Lorentz transformations.

Abstract

The monopole singularity string, infinite direct line in the rest reference frame, is considered as a rigid physical line, and behavior of its geometrical form under the Lorentz transformations is studied. The method to test the form of any rigid line or surface in relativistical terms is based on the use of light signals emitted from the origin of the reference frame. Influence of the motion of the reference frame on the form of singularity line is as follows: (1) in general case, when the line does not go through the origin of the rest reference frame the line in the moving reference frame becomes a hyperbola; (2) in the special case, when the line of singularity goes through the origin of the rest reference frame, the line in the moving reference preserves its form only modified by the relativistical aberration effect.