Notes on Rotation and Rigid Bodies in Relativity Theory

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Abstract
Covariant conditions for rigid-body motion are set up. They are equivalent to those proposed by Born and lead to the linear speed-distance law for the case of rotation about an axis. This result and also a discussion of the transformation equations in going over to a rotating frame of reference are used as arguments for the desirability of retaining the concept of rigid rotation with the linear speed-distance law, contrary to the opinion expressed by Hill. The rotation question is also considered from the standpoint of angular velocity, and one is lead rather naturally to two fluid velocity distributions, one of which was found by Hill. The expression for the spatial distance between two points on a rotating disk obtained by Berenda is derived without the use of the assumption introduced by the latter.