The rotation axis for stationary and axisymmetric space-times

Abstract

A set of 'extended' regularity conditions is discussed which have to be satisfied on the rotation axis if the latter is assumed to be also an axis of symmetry. For a wide class of energy-momentum tensors these conditions can hold at the origin of the Weyl canonical coordinate. For static and cylindrically symmetric space-times the conditions can be derived from the regularity of the Riemann tetrad coefficients on the axis. For stationary space-times, however, the extended conditions do not necessarily hold, even when 'elementary flatness' is satisfied and when there are no curvature singularities on the axis. The authors generalise the result by Davies and Caplan (1971) for cylindrically symmetric stationary Einstein-Maxwell fields, by proving that only Minkowski space-time and a particular magnetostatic solution possess a regular axis of rotation. Further, several sets of solutions for neutral and charged, rigidly and differentially rotating dust are discussed. In most cases only very narrow classes of solutions satisfy the extended requirements.