Transformation equation for frames undergoing non-uniform acceleration such as SHM and rotational motion

TL;DR

This paper extends Lorentz and Rindler transformation equations to non-inertial frames experiencing non-uniform acceleration, including simple harmonic motion and circular motion, with potential applications in physics and astrophysics.

Contribution

It introduces a generalized transformation framework for non-inertial frames undergoing non-uniform acceleration, expanding beyond uniform acceleration cases.

Findings

Derived transformation equations for non-uniform acceleration scenarios.

Applicable to systems undergoing SHM and circular motion.

Provides a foundation for further research in non-inertial reference frames.

Abstract

Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's transformation equations under such a situation. In the present work, we extend the Rindler's equations to a situation where we have in general non-uniform acceleration. After that we consider the non-inertial frame to undergo simple harmonic motion (SHM) and as a second case we consider the non-inertial frame to move uniformly along a circle. This set of transformation equations will have applications in various branches of Physics and in general in Astrophysics.