On nonlinear σ-models arising in (super-)gravity

In a previous paper with Gibbons [1] we derived a list of three dimensional symmetric space sigma-models obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and scalars, Here we give a detailed analysis of their group theoretical structure leading to an abstract parametrization in terms of triangular group elements. This allows for a uniform treatment of all these models. As an interesting application we give a simple derivation of a Quadratic Mass Formula for strictly stationary black holes.