Helical Solutions in Scalar Gravity

TL;DR

This paper constructs rigorous solutions in scalar gravity for rotating bodies with no symmetries, modeling complex dynamical systems like rotating or orbiting bodies, under small gravitational coupling.

Contribution

It introduces a novel method to construct solutions with helical symmetry in scalar gravity, including bodies without any symmetries, advancing the understanding of such configurations.

Findings

Solutions for small G and Ω with helical but no stationary symmetry

Models bodies in steady rotation and orbit without symmetries

Provides a rigorous mathematical framework, pending a conjecture

Abstract

We construct solutions, for small values of $G$ and angular frequency $\Omega$, of special relativistic scalar gravity coupled to ideally elastic matter which have helical but no stationary or axial symmetry. They correspond to a body without any symmetries in steady rotation around one of its axes of inertia, or two bodies moving on a circle around their center of gravity. Our construction is rigorous, but modulo an unproved conjecture on the differentiability of a certain functional.