Multipole Particles in Equilibrium in General Relativity

Axially symmetric static solutions of Einstein's equations with singularities on the $z$ axis are considered. The structure of the singularities is more general than that considered previously by Bergmann, since higher multipole moments are now allowed. The equilibrium conditions for such multipole singularities in an external field are derived. It is shown that solutions having two or more such singularities on the axis may be found in abundance, independently of the signs of the masses of the particles.