Hyperbolic «statics» in space-time
2014jax | PavlovD.G., Kokarev S.S.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia; RSEC Logos, Yaroslavl, Russia, geom2004@mail.ru, logos-center@mail.ru

With using the concept of matter event as a matter source, concentrated on metric sphere of null radius — light cone of Minkowski space-time, — we derive the analog of Coulomb’s law for hyperbolic space-time field, universally acting between events of space-time. The collective field, providing interaction of the world lines of a pair of particles, consists of 3D Coulomb’s part and logarithmic term. We reveal, that the Coulomb’s part is caused by tune balance between causal and geometric properties of space-time (concordance of a two regularization procedures). Equation of motion (in fact — equation of 4D static) for self-consistent configuration of two world lines are integro-differential ones. It is shown, that these equations may be rewritten in the form of relativistic second Newton’s law, where the force and the mass are special parts of universal hyperbolic interaction. We discuss principles and perspectives of using of the device called hyperbolic lense, which is 4D analog of dielectric lense of standard electrostatic.

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