Charged particles in curved space-time

Considering the dynamics of geometry and thematter fields, dynamical equations of geometry and thematter fields are re-derived. The solutions of these equationsare studied. We focus on a charged particle andexplain the axiomatic approach to drive the electromagneticself-force on its motion, then the energy conservationis considered. A new mathematical concept, which isintroduced in axiomatic approach in general, is discussed.