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 ${R}^{2}$ gravity. The metric depends on a new (Buchdahl) parameter $\stackrel{~}{k}$ of higher-derivative characteristic, and recovers the Schwarzschild metric when $\stackrel{~}{k}=0$ . It is shown that the special Buchdahl-inspired metric supports a two-way traversable Morris–Thorne wormhole for $\stackrel{~}{k}\in \left(-1,0\right)$ in which case the Weak Energy Condition is formally violated, a naked singularity for $\stackrel{~}{k}\in \left(-\infty ,-1\right)\cup \left(0,+\infty \right)$ , and a non-Schwarzschild structure for $\stackrel{~}{k}=-1$ .