  In this paper we recall a simple formulation of the stationary electrovacuum
theory in terms of the famous complex Ernst potentials, a pair of functions
which allows one to generate new exact solutions from known ones by means of
the so-called nonlinear hidden symmetries of Lie-Backlund type. This formalism
turned out to be very useful to perform a complete classification of all 4D
solutions which present two spacetime symmetries or possess two Killing
vectors. Curiously enough, the Ernst formalism can be extended and applied to
stationary General Relativity as well as the effective heterotic string theory
reduced down to three spatial dimensions by means of a (real) matrix
generalization of the Ernst potentials. Thus, in this theory one can also make
use of nonlinear matrix hidden symmetries in order to generate new exact
solutions from seed ones. Due to the explicit independence of the matrix Ernst
potential formalism of the original theory (prior to dimensional reduction) on
the dimension D, in the case when the theory initially has D>=5, one can
generate new solutions like charged black holes, black rings and black Saturns,
among others, starting from uncharged field configurations.

High Energy Physics - Theory