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arXiv · 2206.07993

Families of degenerating Poincar\'e-Einstein metrics on $\mathbb{R}^4$

Carlos A. Alvarado·Tristan Ozuch·Daniel A. Santiago
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Abstract

We provide the first example of continuous families of Poincar\'e-Einstein metrics developing cusps on the trivial topology $\mathbb{R}^4$. 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 Pleba\'nski-Demia\'nski. We additionally indicate how to construct similar examples on more complicated topologies.

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Carlos A. Alvarado, Tristan Ozuch, Daniel A. Santiago. 2022-06-16. Families of degenerating Poincar\'e-Einstein metrics on $\mathbb{R}^4$. https://arxiv.org/abs/2206.07993

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