General Relativity: An Introduction for Physicists · Problem 13.22

The Kerr geometry — Hobson, Efstathiou & Lasenby

Physics · kerr-sagnac-bob-simultaneous

Problem

Bob is in a powered spaceship following a circular orbit

r = \text{constant}

in the equatorial plane of the geometry in Exercise 13.21. His angular velocity is such that the component

u_\phi

of his 4-velocity is zero. Using the same arrangement of mirrors as in Exercise 13.21, he performs an experiment similar to Alice's. Show that for Bob the two photons arrive back to him simultaneously.

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