Helically symmetric N-particle solutions in scalar gravity

TL;DR

This paper studies N-particle configurations in a scalar gravity model, proving unique equilibrium states for particles in helical motion and calculating their equilibrium radius using post-Newtonian expansion.

Contribution

It introduces a new analysis of N-body equilibrium configurations in a scalar gravity framework with helical symmetry, providing explicit equilibrium radius calculations.

Findings

Existence of a unique equilibrium configuration.

Explicit computation of equilibrium radius.

Validation within a post-Newtonian approximation.

Abstract

Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles which form an equilateral N-angle and are in helical motion about their common center. We prove that there exists a unique equilibrium configuration and compute the equilibrium radius explicitly in a post-Newtonian expansion.