Spacetime Transformations from a Uniformly Accelerated Frame

TL;DR

This paper develops spacetime transformations for uniformly accelerated frames using Generalized Fermi-Walker transport, providing explicit solutions and metrics, and connecting to existing approaches like Mashhoon's.

Contribution

It introduces a new method to derive local spacetime transformations for uniformly accelerated observers, extending the understanding of accelerated frame metrics and their Lorentz relations.

Findings

Transformations between accelerated frames are Lorentzian.

Derived the metric at any point in a uniformly accelerated frame.

Established connection with Mashhoon's approach.

Abstract

We use Generalized Fermi-Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame $K'$ to an inertial frame $K$. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame.