Traversable Morris–Thorne–Buchdahl wormholes in quadratic gravity

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} 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 (-infty ,-1)cup (0,+infty ), and a non-Schwarzschild structure for tilde{k}=-1.