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

Nonlinear hidden symmetries in General Relativity and String Theory: a matrix generalization of the Ernst potentials