Geometry of an accelerated rotating disk

TL;DR

This paper investigates the geometry of a rotating disk undergoing tangential acceleration within special relativity, employing a kinematic differential system and numerical methods to analyze the relative position of time-like curves.

Contribution

It introduces a detailed geometric analysis of an accelerated rotating disk using a kinematic differential system within special relativity, complemented by numerical integration and comparison with existing studies.

Findings

Numerical solutions for the disk's geometry under acceleration.

Comparison with previous models and results.

Insights into the relativistic geometry of rotating systems.

Abstract

We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the Special Theory of Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in a Fermi reference. A numerical integration of these equations for a generic initial value problem is made up and the results are compared with those obtained in other works.