Extremal limits of rotating black holes

We consider non-extremal, stationary. axion-dilaton solutions to ungauged symmetric supergravity models, obtained by Harrison transformations of the non-extremal Kerr solution. We define a general algebraic procedure, which can be viewed as an Inonu-Wigner contraction of the Noether charge matrix associated with the effective D = 3 sigma-model description of the solution, yielding, through different singular limits, the known BPS and non-BPS extremal black holes (which include the under-rotating non-BPS one The non-extremal black hole can thus be thought of as "interpolating" among these limit-solutions. The algebraic procedure that we define generalizes the known Rasheed-Larsen limit which yielded, in the Kaluza-Klein theory, the first instance of under-rotating extremal solution. As an example of our general result, we discuss in detail the non-extremal solution in the T-3-model, with either q(0), p(1) or p(0), q(1) charges switched on, and its singular limits. Such solutions, computed in D = 3 through the solution-generating technique, is completely described in terms of D = 4 fields, which include the fully integrated vector fields.