Dynamics of test particles and pointlike gyroscopes in the brane world and other 5D models
Abstract
We study the dynamics of test particles and pointlike gyroscopes in 5D manifolds such as those used in the RandallSundrum brane world and noncompact KaluzaKlein models. Our analysis is based on a covariant foliation of the manifold using (3+1)dimensional spacetime slices orthogonal to the extra dimension, and is hence similar to the ArnowittDeserMisner 3+1 split in ordinary general relativity. We derive gauge invariant equations of motion for freely falling test particles in the 5D and 4D affine parametrizations and contrast these results with previous work concerning the socalled ``fifth force.'' Motivated by the conjectured localization of matter fields on a 3brane, we derive the form of the classical nongravitational force required to confine particles to a 4D hypersurface and show that the resulting trajectories are geometrically identical to the spacetime geodesics of Einstein's theory. We then discuss the issue of determining the 5D dynamics of a torquefree spinning body in the pointdipole approximation, and then perform a covariant (3+1)+1 decomposition of the relevant formulas (i.e., the 5D FermiWalker transport equation) for the cases of freely falling and hypersurfaceconfined point gyroscopes. In both cases, the 4D spin tensor is seen to be subject to an anomalous torque. We solve the spin equations for a gyroscope confined to a single spacetime section in a simple 5D cosmological model and observe a cosmological variation of the magnitude and orientation of the 4D spin.
 Publication:

Physical Review D
 Pub Date:
 June 2002
 DOI:
 10.1103/PhysRevD.65.124004
 arXiv:
 arXiv:grqc/0204032
 Bibcode:
 2002PhRvD..65l4004S
 Keywords:

 04.20.Jb;
 11.10.Kk;
 98.80.Hw;
 Exact solutions;
 Field theories in dimensions other than four;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, 2 figures, in press in Phys. Rev. D