Non-extremal black holes, harmonic functions and attractor equations

We present a method which allows one to deform extremal black hole solutions into non-extremal solutions, for a large class of supersymmetric and nonsupersymmetric Einstein-Vector-Scalar type theories. The deformation is shown to work in general when the scalar and vector couplings are encoded by a Hesse potential irrespective of whether the theory is supersymmetric or not. While the line element is dressed with an additional harmonic function, the attractor equations for the scalars remain unmodified in suitable coordinates, and the values of the scalar fields on the outer and inner horizon are obtained from their fixed point values by making specific substitutions for the charges. For a subclass of models, which includes the five-dimensional STU-model, we find explicit solutions.