Autoparallel orbits in Kerr Brans-Dicke spacetimes

TL;DR

This paper investigates the orbital motion of particles in Kerr Brans-Dicke spacetimes, comparing auto-parallel worldlines under different metric-compatible connections to distinguish the effects of torsion.

Contribution

It introduces a method to analyze particle orbits using auto-parallel worldlines in Kerr Brans-Dicke geometries, considering both torsion-free and torsion-inclusive connections.

Findings

Differentiates between Levi-Civita and torsionful connections in particle motion.

Provides a framework to potentially discriminate between geometric structures in scalar-tensor theories.

Analyzes bounded orbital motion in complex spacetime backgrounds.

Abstract

The bounded orbital motion of a massive spinless test particle in the background of a Kerr Brans-Dicke geometry is analysed in terms of worldlines that are auto-parallels of different metric compatible spacetime connections. In one case the connection is that of Levi-Civita with zero-torsion. In the second case the connection has torsion determined by the gradient of the Brans-Dicke background scalar field. The calculations permit in principle to discriminate between these possibilities.