Traversable Morris-Thorne-Buchdahl wormholes in quadratic gravity

The special Buchdahl-inspired metric obtained in a recent paper [Phys. Rev. D 107, 104008 (2023)] describes asymptotically flat spacetimes in pure ${\mathcal{R}}^2$ gravity. The metric depends on a new (Buchdahl) parameter $\tilde{k}$ of higher-derivative characteristic, and recovers the Schwarzschild metric when $\tilde{k}=0$. It is shown that the special Buchdahl-inspired metric supports a two-way traversable Morris-Thorne wormhole for $\tilde{k}\in (-1,0)$ in which case the Weak Energy Condition is formally violated, a naked singularity for $\tilde{k}\in (-\mathrm{\infty },-1)\cup (0,+\mathrm{\infty })$, and a non-Schwarzschild structure for $\tilde{k}=-1$.