On the integrability of halo dipoles in gravity

TL;DR

This paper investigates the integrability of halo dipole components in gravity, demonstrating that while Newtonian dynamics remains integrable, relativistic effects induce chaos due to halo dipoles.

Contribution

The authors extend a relativistic model to include halo dipoles and analyze their impact on orbital dynamics, revealing intrinsic relativistic chaos.

Findings

Newtonian orbits are integrable in the presence of halo dipoles.

Relativistic orbits exhibit chaos due to halo dipoles.

Halo dipoles cause intrinsic relativistic gravitational effects.

Abstract

We stress that halo dipole components are nontrivial in core-halo systems in both Newton's gravity and General Relativity. To this end, we extend a recent exact relativistic model to include also a halo dipole component. Next, we consider orbits evolving in the inner vacuum between a monopolar core and a pure halo dipole and find that, while the Newtonian dynamics is integrable, its relativistic counterpart is chaotic. This shows that chaoticity due only to halo dipoles is an intrinsic relativistic gravitational effect.