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We provide the first example of continuous families of Poincar\'e-Einsteinmetrics developing cusps on the trivial topology $\mathbb{R}^4$. We alsoexhibit families of metrics with unexpected degenerations in their conformalinfinity only. These are obtained from the Riemannian version of an ansatz ofDebever and Pleba\'nski-Demia\'nski. We additionally indicate how to constructsimilar examples on more complicated topologies.

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