General Relativity: An Introduction for Physicists · Problem 10.10

Experimental tests of general relativity — Hobson, Efstathiou & Lasenby

Physics · geodesic-precession-angle-general

Problem

A gyroscope in a circular orbit of radius

r

in the equatorial plane of the Schwarzschild geometry has its spatial spin vector

\vec{s}

also lying in the equatorial plane. Show that, after one complete orbit, the angle between the initial and final directions of the spatial spin vector is given by

\alpha = 2\pi\left[1 - (1 - 3\mu/r)^{1/2}\right],

irrespective of the initial direction of the spin vector. Does this still hold if the original spatial spin vector does not lie in the plane of the orbit?

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