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arXiv · 2606.24761

On Chen-Teo geometries with cosmological constant

Bernardo Araneda
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Abstract

The Chen-Teo geometry is a Riemannian, Ricci-flat ALF 4-manifold, containing an AF gravitational instanton that gives the first counterexample to the Euclidean black hole uniqueness conjecture. We investigate the problem of constructing an Einstein analogue with a non-zero cosmological constant $\lambda$. We show that the solution is either the Pleba\'nski-Demia\'nski metric with $\lambda$, or it has an anti-self-dual Weyl tensor. We study the latter case in detail: we prove that for $\lambda<0$, there is a conformal infinity separating two asymptotically hyperbolic metrics; we show that one of them is globally conformal to an ALE scalar-flat K\"ahler metric; we construct gravitational instantons with different topologies; and we show that the geometry is a 4-pole solution in the Calderbank-Pedersen classification.

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Bernardo Araneda. 2026-06-23. On Chen-Teo geometries with cosmological constant. https://arxiv.org/abs/2606.24761

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