Note on the form of the metric for an isolated vortex in general relativity.

Calling a metric semidiagonal if it has a single off-diagonal element g t, we show that the stationary interior solution for a cylindrically symmetrical perfect fluid possessing an angular momentum cannot have a semidiagonal metric, unless the motion of the fluid particles is purely rotational around the axis of symmetry. A discussion is given of the relativistic spherical vortex in flat space, with a view of seeking a solution for such an isolated vortex in which gravitation is not neglected.