Uniform Acceleration in General Relativity

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.

19 pages. arXiv admin note: text overlap with arXiv:1105.0492

References in corpus (2)

• Making the Relativistic Dynamics Equation Covariant: Explicit Solutions for Motion under a Constant Force
• Spacetime Transformations from a Uniformly Accelerated Frame

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