Global Dynamical time for Binary Point-Like Particle Systems

MORESCHI, OSVALDO M.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2020 p. 1 - 26

0219-8878

A geometrical construction for a global dynamicaltime for binary point-like particle systems,modeled by relativistic equations of motions, is presented.Thus, we provide a convenient tool for the calculationof the dynamics of recent models for the dynamicsof black holes that use individual proper times.The construction is naturally based on the local Lorentziangeometry of the spacetime one is considering.Although in this presentation we are dealing with theMinkowskian spacetime; the construction is useful forgravitational models that have as a seed Minkowskispacetime.We present the discussion for a binary system, butthe construction is obviously generalizable tomultiple particle systems.The calculations are organized in terms of the orderof the corresponding relativistic forces.In particular we improve on the Darwin and Landau-Lifshitz approaches, for the case of electromagneticsystems.We discuss the possibility of a Lagrangian treatment of the retardedeffects, depending on the nature of the relativistic forces.The higher order contractions are based on a Runge-Kutta typeprocedure, which is used to calculate the quantitiesat the required retarded time,by increasing evaluations of the forces at intermediatetimes.We emphasize the difference between approximation ordersin field equations and approximation orders in retarded effects in the equations of motion.We show this difference by applying our constructionto the binary electromagnetic case.