Spacetime Ehlers group: transformation law for the Weyl tensor

Abstract

The spacetime Ehlers group, which is a symmetry of the Einstein vacuumfield equations for strictly stationary spacetimes, is defined and analysedin a purely spacetime context (without invoking the projectionformalism). In this setting, the Ehlers group finds its natural descriptionwithin an infinite-dimensional group of transformations that mapsLorentz metrics into Lorentz metrics and which may be of independentinterest. The Ehlers group is shown to be well defined independently of thecausal character of the Killing vector (which may become null on arbitraryregions). We analyse which global conditions are required on thespacetime for the existence of the Ehlers group. The transformation lawfor the Weyl tensor under Ehlers transformations is obtainedexplicitly.This allows us to study where, and under what circumstances, curvaturesingularities in the transformed spacetime will arise. The results of thepaper are applied to obtain a local characterization of the Kerr-NUTmetric.