Hyperbolic statics in space-time

Abstract

Based on the concept of a material event as an elementary material source that is concentrated on a metric sphere of zero radius—a light cone of Minkowski space-time, we deduce an analog of Coulomb’s law for a hyperbolic space-time field universally acting between space-time events. The collective field that provides interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb part and a logarithmic addition. We find that the Coulomb part depends on a fine balance between the causal and geometric space-time characteristics (a concordance of two regularizations).