General Relativity: An Introduction for Physicists · Problem 17.26

Linearised general relativity — Hobson, Efstathiou & Lasenby

Physics · lens-thirring-gyroscope-precession-angular-velocity

Problem

A gyroscope is in orbit about the massive rotating body in Exercise 17.23. Use your answer to Exercise 17.25 to show that the precessional angular velocity vector of the gyroscope is given by Ω⃗=Gc2∣x⃗∣3[3(J⃗⋅x^)x^−J⃗],\vec{\Omega} = \frac{G}{c^2|\vec{x}|^3}\left[3(\vec{J}\cdot\hat{x})\hat{x} - \vec{J}\right], where x⃗\vec{x} is the position vector of the gyroscope relative to the centre of the massive body. Show that this result agrees with that derived in Section 13.20 when x⃗\vec{x} points along J⃗\vec{J}.

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