Multipolar Solutions

Abstract: A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they can be used to describe the exterior gravitational field of an arbitrarily rotating mass distribution endowed with an electromagnetic field. The presence of gravitational multipoles completely changes the structure of the spacetime because of the appearance of naked singularities in a confined spatial region. The possibility of covering this region with interior solutions is analyzed in the case of a particular solution with quadrupole moment.