Locating Minimal Surfaces in Geometrostatic Manifolds

Abstract: In 1963 Brill and Lindquist asked where one might find the apparent horizons of charged black holes in geometrostatic manifolds that arise as time symmetric solutions to vacuum Einstein Maxwell constraint equations. These manifolds are asymptotically flat with nonnegative scalar curvature and the apparent horizons are minimal surfaces. In joint work with Iva Stavrov, we locate these minimal surfaces where the black holes are sufficiently far apart relative to their respective masses. Upcoming joint work with Shubham Dwivedi, Rohit Jain, and Tobias Schmid concerning the setting with one massive black hole surrounded by smaller ones will be announced.