On Universality of Ergoregion Mergers

We study mergers of ergoregions in $d+1$-dimensional vacuum gravity. At the merger point, where the ergosurfaces bounding each ergoregion just touch, solutions exhibit universal behavior when there is rotation only in one plane: the angle between the merging ergosurfaces depends only on the symmetries of the solution, not on any other details of the configuration. We show that universality follows from the fact that the relevant component of Einstein's equation reduces to Laplace equation at the point of merger. Thus ergoregion mergers mimic mergers of Newtonian equipotentials and have similar universal behavior. For solutions with rotation in more than one plane, universality is lost. We demonstrate universality and non-universality in several explicit examples.