Sigma-model approaches to exact solutions in higher-dimensional gravity and supergravity

28 pages, 1 figure, talk presented at the WE Heraeus Seminar on Models of Gravity in Higher Dimenions: From Theory to Experimental Search, Bremen, 25-29.8.2008Classical gravitating field theories reduced to three dimensions admit manifest gauge invariances and hidden symmetries, which together make up the invariance group G of the theory. If this group is large enough, the target space is a symmetric space G/H. New solutions may be generated by the action of invariance transformations on a seed solution. Another application is the construction of multicenter solutions from null geodesics of the target space. After a general introduction on this sigma-model approach, I will discuss the case of five-dimensional gravity, with invariace group SL(3,R), and minimal five-dimensional supergravity, with invariance group G_{2(2)}. I will also describe recent attempts at the generation of new charged rotating black rings