Hyperbolic statics in space-time

TL;DR

This paper derives a Coulomb-like law for hyperbolic space-time fields based on the concept of material events on light-cones, revealing a combined Coulomb and logarithmic interaction component.

Contribution

It introduces a novel hyperbolic space-time field model using material events on light-cones, extending classical Coulomb law to a relativistic context.

Findings

The interaction includes a Coulomb and a logarithmic term.

The Coulomb part depends on causal and geometric regularizations.

The model unifies causal structure with geometric properties of space-time.

Abstract

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