Abstract
We extend de la Fuente and Romero’s (Gen Relativ Gravit 47:33, 2015) 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.
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Acknowledgments
We would like to thank L. Horwitz, B. Mashhoon, F. Hehl, Y. Itin, S. Lyle, and Ø. Grøn for challenging remarks which have helped to clarify some of the ideas presented here. This work was partially supported by the German-Israeli Foundation for Scientific Research and Development: GIF No. 1078-107.14/2009.
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Friedman, Y., Scarr, T. Uniform acceleration in general relativity. Gen Relativ Gravit 47, 121 (2015). https://doi.org/10.1007/s10714-015-1966-5
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DOI: https://doi.org/10.1007/s10714-015-1966-5