The reaction-free trajectories of a classical point charge

It is well-known that a classical point charge in 1+1 D hyperbolic motion in space and time is reaction-free. But this is a special case of a larger set of reaction-free trajectories that in general are curved paths through space, i.e. in 2+1 D. This note catalogs the full family of reaction-free trajectories, giving a geometrical interpretation by which means the curved path possibility is easily related to the better known case of hyperbolic motion in 1+1 D. Motivated by the geometry, it is shown how the catalog of motions can be naturally extended to include the possibility of lossless reaction-free closed spatial orbits that turn out to be classical pair creation and destruction events. keywords: Lorentz-Dirac; Abraham; von Laue; radiation-reaction; superluminal; tachyon PACS: 03.50.De 41.60.-m MSC: 78A35 78A40 1 The Abraham von Laue vector In Heaviside units with c = 1, the Lorentz-Abraham-Dirac equation for a classical charge of mass m is ma = fext + Γ (1) where fext is the external force 4-vector, and Γ is the von Laue or Abraham 4-vector given by Γ = 2e 3 (