Transport along Null Curves

Details Transport along Null Curves Transport along Null Curves

2000-05-22

arxiv.org/abs/gr-qc/0005096v1

J.Phys.A33:2895,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex 17 pages, no figures

Scientific paper

10.1088/0305-4470/33/14/318

Fermi Transport is useful for describing the behaviour of spins or gyroscopes following non-geodesic, timelike world lines. However, Fermi Transport breaks down for null world lines. We introduce a transport law for polarisation vectors along non-geodesic null curves. We show how this law emerges naturally from the geometry of null directions by comparing polarisation vectors associated with two distinct null directions. We then give a spinorial treatment of this topic and make contact with the geometric phase of quantum mechanics. There are two significant differences between the null and timelike cases. In the null case (i) The transport law does not approach a unique smooth limit as the null curve approaches a null geodesic. (ii) The transport law for vectors is integrable, i.e the result depends only on the local properties of the curve and not on the entire path taken. However, the transport of spinors is not integrable: there is a global sign of topological origin.

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