Equilibrium states in the quadruple-Kerr solution (Q1431727)

The article studies a `quadruple-Kerr' solution obtained as a special case of multi-soliton solutions to the Ernst equation. These solutions have in general Kerr-type horizons or a disk-like singularity. There is typically a singular axis between the horizons, a so-called Weyl strut, or in the case of negative masses, a ring singularity. The conditions for equilibrium equations, i.e. configurations with a regular axis in the complement of the horizons, are studied numerically. It is found that there are no equilibrium configurations for regular black holes: there are either singular rings or disks in these spacetimes according to the expectation that there is no regular multi-black-hole solution of the stationary vacuum Einstein equations.