Families of degenerating Poincaré–Einstein metrics on ℝ4
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10455_2023_Article_9923.pdf
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Author(s)
Alvarado, Carlos A.
Ozuch, Tristan
Santiago, Daniel A.
Date Issued
December 6, 2023
Publisher
Springer Netherlands
Citation
Annals of Global Analysis and Geometry. 2023 Dec 06;65(1):5
Version
Final published version
Abstract
Abstract
We provide the first example of continuous families of Poincaré–Einstein metrics developing cusps on the trivial topology
$$\mathbb {R}^4$$
R
4
. We also exhibit families of metrics with unexpected degenerations in their conformal infinity only. These are obtained from the Riemannian version of an ansatz of Debever and Plebański–Demiański. We additionally indicate how to construct similar examples on more complicated topologies.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s10455-023-09923-y
