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Four dimensional supergravity theories whose scalar manifold is a symmetriccoset manifold U[D=4]/Hc are arranged into a finite list of Tits Satakeuniversality classes. Stationary solutions of these theories, sphericallysymmetric or not, are identified with those of an euclidian three-dimensionalsigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and theextremal ones are associated with H* nilpotent orbits in the K* representationemerging from the orthogonal decomposition of the algebra U[D=3] with respectto H*. It is shown that the classification of such orbits can always be reducedto the Tits-Satake projection and it is a class property of the Tits Satakeuniversality classes. The construction procedure of Bossard et al of extremalmulticenter solutions by means of a triangular hierarchy of integrableequations is completed and converted into a closed algorithm by means of ageneral formula that provides the transition from the symmetric to the solvablegauge. The question of the relation between H* orbits and charge orbits W ofthe corresponding black holes is addressed and also reduced to thecorresponding question within the Tits Satake projection. It is conjecturedthat on the vanishing locus of the Taub-NUT current the relation betweenH*-orbit and W-orbit is rigid and one-to-one. All black holes emerging frommulticenter solutions associated with a given H* orbit have the same W-type.For the S^3 model we provide a complete survey of its multicenter solutionsassociated with all of the previously classified nilpotent orbits of sl(2) xsl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits ofthis model that might provide a paradigm for the analogous classification inall the other Tits Satake universality classes.

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes