Gluing charged black holes into de Sitter space
Markus Verlemann
TL;DR
This work extends Hintz's cosmological gluing framework to the Einstein–Maxwell system with Λ>0 by embedding multiple charged black holes (RN–dS and KN–dS) into de Sitter space at the conformal boundary. Using 0-geometry and cohomological/indicial analysis, the authors derive precise charge and mass balance conditions that permit gluing, and they refine the construction to produce a formal infinite-order solution via an exactness argument before passing to a true solution with a DeTurck/Lorenz gauge. The results are extended to rotating black holes (KNdS), where rotation modifies the balance through effective charges and masses, yielding a comprehensive gluing framework for charged (and rotating) black holes in de Sitter backgrounds. Overall, the paper provides a rigorous method to construct multi-black-hole spacetimes in cosmological settings, with explicit solvability conditions and a streamlined path to actual solutions in the Einstein–Maxwell theory.
Abstract
We extend Hintz's cosmological black hole gluing result to the Einstein-Maxwell system with positive cosmological constant by gluing multiple Reissner-Nordström 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.