The spacetime Ehlers group, which is a symmetry of the Einstein vacuum field
equations for strictly stationary spacetimes, is defined and analyzed in a
purely spacetime context (without invoking the projection formalism). In this
setting, the Ehlers group finds its natural description within an infinite
dimensional group of transformations that maps Lorentz metrics into Lorentz
metrics and which may be of independent interest. The Ehlers group is shown to
be well defined independently of the causal character of the Killing vector
(which may become null on arbitrary regions). We analyze which global
conditions are required on the spacetime for the existence of the Ehlers group.
The transformation law for the Weyl tensor under Ehlers transformations is
explicitly obtained. This allows us to study where, and under which
circumstances, curvature singularities in the transformed spacetime will arise.
The results of the paper are applied to obtain a local characterization of the
Kerr-NUT metric.Comment: LaTeX, 25 pages, no figures, uses Amstex. Accepted for publication in
Classical and Quantum Gravit
