A unified approach to infinitesimal Loewner and Geroch transformations and the Ernst and Einstein-Maxwell equations

It is demonstrated that the dual Ernst equation of general relativity constitutes a stationary Loewner system. In an analogous manner, it is shown that the Einstein-Maxwell equations for stationary axisymmetric space-times and their extension to Einstein's equations coupled with an arbitrary number of U(1) gauge fields may be interpreted as generalized Loewner systems. Moreover, it is recorded that the base Geroch transformation for the (dual) Ernst equation may be located in a class of infinitesimal Baecklund transformations introduced by Loewner in 1952. A Geroch-type transformation for a generic class of 2+1-dimensional Loewner systems is set down and it is shown how the base Geroch and Hoenselaers-Kinnersley-Xanthopoulos transformations are naturally retrieved. (author)