Gluing charged black holes into de Sitter space

Abstract

We extend Hintz's cosmological black hole gluing result to the Einstein-Maxwell system with positive cosmological constant by gluing multiple Reissner-Nordstr\"om or Kerr--Newman--de Sitter black holes into neighbourhoods of points in the conformal boundary of de Sitter space. We determine necessary and sufficient conditions on the black hole parameters -- related to Friedrich's conformal constraint equations -- for this gluing to be possible. We also improve the original gluing method slightly by showing that the construction of a solution in Taylor series may be accomplished using an exactness argument, eliminating the need for an early gauge-fixing.