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We study the dynamics of test particles and pointlike gyroscopes in 5Dmanifolds like those used in the Randall-Sundrum brane world and non-compactKaluza-Klein models. Our analysis is based on a covariant foliation of themanifold using 3+1 dimensional spacetime slices orthogonal to the extradimension, and is hence similar to the ADM 3+1 split in ordinary generalrelativity. We derive gauge invariant equations of motion for freely-fallingtest particles in the 5D and 4D affine parameterizations and contrast theseresults with previous work concerning the so-called ``fifth force''. Motivatedby the conjectured localization of matter fields on a 3-brane, we derive theform of the classical non-gravitational force required to confine particles toa 4D hypersurface and show that the resulting trajectories are geometricallyidentical to the spacetime geodesics of Einstein's theory. We then discuss theissue of determining the 5D dynamics of a torque-free spinning body in thepoint-dipole approximation, and then perform a covariant (3+1)+1 decompositionof the relevant formulae (i.e. the 5D Fermi-Walker transport equation) for thecases of freely-falling and hypersurface-confined point gyroscopes. In bothcases, the 4D spin tensor is seen to be subject to an anomalous torque. Wesolve the spin equations for a gyroscope confined to a single spacetime sectionin a simple 5D cosmological model and observe a cosmological variation of themagnitude and orientation of the 4D spin.Comment: 13 pages, 2 figures, in press in Phys. Rev.

Dynamics of test particles and pointlike gyroscopes in the brane world and other 5D models