Spatial geometry of the rotating disk and its non-rotating counterpart

Abstract

A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry of their proper space is hyperbolic. This has interesting consequences concerning their interpretation of the geometry of a non-rotating disk having the same radius. The influence of clock synchronization on spatial measurements is discussed.

10 pages, 3 figures, this is the version accepted by American Journal of Physics; I had to remove the special relativity part, which one of the referees did not like; it is still available in v1

References in corpus (3)

• The equivalence principle, uniformly accelerated reference frames, and the uniform gravitational field
• Synchronization Gauges and the Principles of Special Relativity
• Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times

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• Observers and Splitting Structures in Relativistic Electrodynamics
• Classroom reconstruction of the Schwarzschild metric
• Spatial geometry of charged rotating and non-rotating rings in rotating and non-rotating frames
• A Simple Relativity Solution to the Bell Spaceship Paradox