The 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 like those used in the Randall-Sundrum brane world and non-compact Kaluza-Klein 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 ADM 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 parameterizations and contrast these results with previous work concerning the so-called ``fifth force''. Motivated by the conjectured localization of matter fields on a 3-brane, we derive the form of the classical non-gravitational 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 torque-free spinning body in the point-dipole approximation, and then perform a covariant (3+1)+1 decomposition of the relevant formulae (i.e. the 5D Fermi-Walker transport equation) for the cases of freely-falling and hypersurface-confined 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.

13 pages, 2 figures, in press in Phys. Rev. D

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• Null Geodesics in Five Dimensional Manifolds
• Black holes on thick branes
• Thick branes and Gauss-Bonnet self-interactions
• Null Geodesics in Brane World Universe
• The Structure of the Big Bang from Higher-Dimensional Embeddings
• Does The Force From an Extra Dimension Contradict Physics in 4D?
• Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity
• Dilaton Black Holes on Thick Branes

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• Geodetic Precession in Squashed Kaluza-Klein Black Hole Spacetimes
• Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim
• Invariant definition of rest mass and dynamics of particles in 4D from bulk geodesics in brane-world and non-compact Kaluza-Klein theories
• Fifth force from fifth dimension: a comparison between two different approaches
• Wesson's IMT with a Weylian bulk
• Embeddings for General Relativity
• Brane Vector Dynamics from Embedding Geometry
• Time-dependent extra dimension and higher-dimensional modifications to the matter content in FRW spacetimes
• Non-integrability and Mach's principle in Induced Matter Theory
• Dark matter and cosmic acceleration from Wesson's IMT
• The principle of least action for test particles in a four-dimensional spacetime embedded in 5D
• On the classical confinement of test particles to a thin 3-brane in the absence of non-gravitational forces
• Proper time and conformal problem in Kaluza-Klein theory