On the gravitational field of static and stationary axial symmetric bodieswith multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo sol ution of the Einstein equations in terms of bars. We find that each multi-p ole corresponds to the Newtonian potential of a bar with linear density pro portional to a Legendre polynomial. We use this fact to find an integral re presentation of the gamma function. These integral representations are used in the context of the inverse scattering method to find solutions associat ed with one or more rotating bodies each with their own multi-polar structu re.