Uniform Acceleration in General Relativity

TL;DR

This paper generalizes the concept of uniform acceleration in curved spacetime, providing explicit solutions in flat spacetime, and applies these to charged particle motion, connecting to the Lorentz-Abraham-Dirac equation.

Contribution

It extends the definition of uniform acceleration to full Lorentz covariance in curved spacetime and derives related transformations and solutions.

Findings

Explicit solutions for uniform acceleration in flat spacetime.

Derived velocity and acceleration transformations between accelerated and inertial frames.

Connected acceleration transformations to the Lorentz-Abraham-Dirac equation for charged particles.

Abstract

We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit solutions. We use generalized Fermi-Walker transport to parallel transport the Frenet basis along the trajectory. In flat spacetime, we obtain velocity and acceleration transformations from a uniformly accelerated system to an inertial system. We obtain the time dilation between accelerated clocks. We apply our acceleration transformations to the motion of a charged particle in a constant electromagnetic field and recover the Lorentz-Abraham-Dirac equation.