Class of Einstein-Maxwell-dilaton-axion space-times

We use the harmonic maps ansatz to find exact solutions of the Einstein- Maxwell-dilaton-axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions Sp(4, R) similar to O(5). We find solutions of the EMDA field equations for the one- and two-dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find spacetimes that generalize the Schwarzschild solution with dilaton, axion, and electromagnetic fields.