Class of Einstein-Maxwell dilatons, an ansatz for new families of rotatingsolutions

The functional potential formalism is used to analyse stationary axisymmetr ic spaces in Einstein-Maxwell-dilaton theory. Performing a Legendre transfo rmation, a Hamiltonian is obtained, which allows us to rewrite the dynamica l equations in terms of three complex functions only. Using an ansatz resem bling the one used by the harmonic maps ansatz, we express these three func tions in terms of the harmonic parameters, studying the cases where these p arameters are real, and when they are complex. For each case, the set of eq uations in terms of these harmonic parameters is derived, and several class es of solutions to the Einstein-Maxwell equations with arbitrary coupling c onstant to a dilaton field are presented. Most of the known solutions of ch arged and dilatonic black holes are contained as special cases and can be n on-trivially generalized in different ways.