Black hole gluing in de Sitter space
© 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 met...
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| Format: | Article |
| Language: | English |
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Informa UK Limited
2021
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| Online Access: | https://hdl.handle.net/1721.1/134040 |
| _version_ | 1811077086231658496 |
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| author | Hintz, Peter |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Hintz, Peter |
| author_sort | Hintz, Peter |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T10:37:40Z |
| format | Article |
| id | mit-1721.1/134040 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:37:40Z |
| publishDate | 2021 |
| publisher | Informa UK Limited |
| record_format | dspace |
| spelling | mit-1721.1/1340402023-12-14T15:31:06Z Black hole gluing in de Sitter space Hintz, Peter Massachusetts Institute of Technology. Department of Mathematics © 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. 2021-10-27T19:57:45Z 2021-10-27T19:57:45Z 2021 2021-05-20T14:49:47Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134040 en 10.1080/03605302.2020.1871368 Communications in Partial Differential Equations Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Informa UK Limited arXiv |
| spellingShingle | Hintz, Peter Black hole gluing in de Sitter space |
| title | Black hole gluing in de Sitter space |
| title_full | Black hole gluing in de Sitter space |
| title_fullStr | Black hole gluing in de Sitter space |
| title_full_unstemmed | Black hole gluing in de Sitter space |
| title_short | Black hole gluing in de Sitter space |
| title_sort | black hole gluing in de sitter space |
| url | https://hdl.handle.net/1721.1/134040 |
| work_keys_str_mv | AT hintzpeter blackholegluingindesitterspace |