Traversable Morris–Thorne–Buchdahl wormholes in quadratic gravity

Abstract

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