The equation of motion for a classical charged point particle in curved space-time is given by the generalized Lorentz-Abraham-Dirac equation. This equation contains a nonlocal term called the tail term, which consists of an integral over the entire past history of the particle. I explain how this term comes about, and shows how it can be divided into 2 qualitatively different effects: A dispersion effect, which is connected to violation of Huygens' principle and sub-lightspeed propagation of the field, and an independent topological effect.
To illustrate these, I also show a tail term comes about about from the cases spesific cases of 1. Flat 3+1-dimensional space-time with a cyclic dimension, 2. Flat 4+1-dimensional space-time, 3. matter, radiation and LIVE-dominated homogenous and isotropic universes, and 4. Around a black hole.