Moduli Space of Stationary Axisymmetric Vacuum Solutions

The classification theorems discussed in the previous chapter determine the conditions which specify the stationary and axisymmetric spacetimes uniquely. However, they contain no information about the existence of such spacetimes which are completely regular in the domain of outer communications. We need further analysis in order to constrain the moduli space of the regular solutions. In this chapter we develop a procedure for describing the moduli space of the regular stationary and axisymmetric solutions in vacuum applying it on the classes of solutions associated with the simplest interval structures.