Quantum fields on glued spacetimes
Summary
In a 2020 paper, Hintz showed that one can perturb the de Sitter metric in such a
way that it solves the Einstein equations and that in before-hand specified subregions
of spacetime, its form is exactly Schwarzschild-de Sitter or Kerr-de Sitter. For this, he
developed a method of gluing Schwarzschild-de Sitter or Kerr-de Sitter metrices onto a de
Sitter background.
In this thesis, we first review Hintz’s gluing construction and the resulting class of
spacetimes. We then turn to the analysis of the Klein–Gordon equation on such glued
spacetimes. For classical Klein–Gordon fields, we show that given local solutions near the
black hole regions, one can glue these together into a global solution without changing the
behavior near the black hole. Secondly, we extend this result to quantum Klein–Gordon
fields by gluing appropriate Cauchy data. Lastly, we will sketch how to push this quantum
gluing all the way to the conformal boundary of the manifold.