Monopole-quadrupole static axisymmetric solutions of Einstein field equations

An infinite family of exact solutions of the Einstein vacuum equations for the static case with axial symmetry is presented in an explicit form. Each solution of this family contains two arbitrary parametersM andQ that represent the mass and quadrupole moment of the source. In addition, each solution can be interpreted physically as the pure relativistic quadrupole correction to the Schwarzschild solution at a given multipole order.