Black hole gluing in de Sitter space
Name
2001.10401.pdf
Description
Submitted version
Size
687.12 KB
Format
Adobe PDF
Checksum (MD5)
9359b0d376811373f38832f3518182c6
Author(s)
Hintz, Peter
Date Issued
2021
Journal
Communications in Partial Differential Equations
Publisher
Informa UK Limited
Version
Original manuscript
Abstract
© 2021 Taylor & Francis Group, LLC. We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild–de Sitter or Kerr–de Sitter black hole metrics into neighborhoods of points on the future conformal boundary of de Sitter space, under certain balance conditions on the black hole parameters. We give a self-contained treatment of solving the Einstein equation directly for the metric, given the scattering data we encounter at the future conformal boundary. The main step in the construction is the solution of a linear divergence equation for trace-free symmetric 2-tensors; this is closely related to Friedrich’s analysis of scattering problems for the Einstein equation on asymptotically simple spacetimes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/03605302.2020.1871368
