Dilatonic Probe, Force Balance and Gyromagnetic Ratio

TL;DR

This paper derives the equations of motion for a dilatonic test body using a dimensional reduction approach, analyzing force balance, spin interactions, and the gyromagnetic ratio, revealing a saturation of a Bogomol'nyi bound.

Contribution

It provides a novel derivation of the dilatonic test body's equations of motion via dimensional reduction, connecting force balance and gyromagnetic ratio to fundamental bounds.

Findings

Force balance condition leads to Bogomol'nyi bound saturation.

Gyromagnetic ratio of the test body is derived.

Dilatonic effects are analyzed through dimensional reduction.

Abstract

Following the Papapetrou-Dixon-Wald procedure we derive the equation of motion for a dilatonic test body(probe) with the dilaton coupling $\alpha = {\sqrt {p/(2+p)}}$ in four dimension. Since the dilatonic freedom sometimes comes from extra dimensions, it is best to derive the EOM by a dimensional reduction from $(p+4)-$dimensions. We discuss about the force balance up to the gravitational spin-spin interactions via the probe technique. The force balance condition yields the saturation of a Bogomol'nyi bound and the gyromagnetic ratio of the test body.