Dilatonic Probe, Force Balance and Gyromagnetic Ratio

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.