Traversable wormholes with double layer thin shells in quadratic gravity

In quadratic gravity, the junction conditions are six in number and permit the appearance of double layer thin shells. Double layers arise typically in theories with dipoles, i.e., two opposite charges, such as electromagnetic theories, and appear exceptionally in gravitational theories, which are theories with a single charge. We explore this property of the existence of double layers in quadratic gravity to find and study traversable wormholes in which the two domains of the wormhole interior region, where the throat is located, are matched to two vacuum domains of the exterior region via the use of two double layer thin shells. The quadratic gravity we use is essentially given by a $$R+\alpha R^2$$ R + α R 2 Lagrangian, where R is the Ricci scalar of the spacetime and $$\alpha $$ α is a coupling constant, plus a matter Lagrangian. The null energy condition, or NEC for short, is tested for the whole wormhole spacetime. The analysis shows that the NEC is satisfied for the stress-energy tensor of the matter in the whole wormhole interior region, notably at the throat, and is satisfied for some of the stress–energy tensor components of the matter at the double layer thin shell, but is not satisfied for some other components, namely, the double layer stress–energy distribution component, at the thin shell. This seems to mean that the NEC is basically impossible, or at least very hard, to be satisfied when double layer thin shells are present. Single layer thin shells are also admitted within the theory, and we present thin shell traversable wormholes, i.e., wormholes without interior, with a single layer thin shell at the throat for which the corresponding stress–energy tensor satisfies the NEC, that are asymmetric, i.e., with two different vacuum domains of the exterior region joined at the wormhole throat.