  Within the framework of general relativity, in some cases at least, it is a
delicate and interesting question just what it means to say that an extended
body is or is not "rotating". It is so for two reasons. First, one can easily
think of different criteria of rotation. Though they agree if the background
spacetime structure is sufficiently simple, they do not do so in general.
Second, none of the criteria fully answers to our classical intuitions. Each
one exhibits some feature or other that violates those intuitions in a
significant and interesting way. The principal goal of the paper is to make the
second claim precise in the form of a modest no-go theorem.
