The Relativity Equations of Uniformly Accelerating Frames of Reference

Abstract

The work presented here is an extension of the work done in the article titled “The Conjugate Frame Method Relativity” [1]. In that work, we considered a moving reference frame that traveled at a constant speed v in a flat or curved space-time manifold. The moving reference frame traveled along a geodesic trajectory in a direction that was either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame was equal to zero. In this work, we consider a moving reference frame that travels with a uniformly changing speed v in a flat or curved space-time manifold. The moving reference frame travels along a geodesic trajectory in a direction that is either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame is a constant that is greater than or equal to zero. The Augmented Conjugate Frame Method is utilized in this work to derive the relativity equations of uniformly accelerating reference frames. These equations can apply to objects that are uniformly accelerated by gravitational, electric, or magnetic fields; as well as by other means, such as rocket propulsion. The relativity equations derived in this work reduce to the equations of Special Relativity when the moving reference frame has a zero scalar acceleration. The Augmented Conjugate Frame Method uses only scalar quantities in the derivation of the relativity equations of uniformly accelerating frames of reference.