“…Since the Ehlers group is developed within this formalism, it becomes necessary to adopt a different approach to this problem, or at least define the Ehlers group in such a way that they include the case of null Killing vectors. As stated on [39], there were examples suggesting that it would be possible to extend the Ehlers group to encompass null Killing vectors, and it is shown in [39] that this is indeed possible, if one no longer works in the projection formalism and instead works in a spacetime setting, i.e., using only spacetime objects. Moreover, it is shown that the Ehlers group can be included within an infinite-dimensional group of transformations mapping Lorentzian metrics into Lorentzian metrics.…”