a lot of attention has been paid to their geometrical properties and it is believed that quantum mechanics could provide such an exotic matter, since in the Casimir effect the null, weak, strong, and dominant energy conditions are all violated [^1]. Another empirical fact that supports this kind of exotic matter is the accelerated expansion of the universe, which can be explained by a matter that violates at least one of the energy conditions [@Nojiri20031; @Straumann:2002he]. Some methods have been developed to distinguish the gravitational lensing due to a wormhole from the ones caused by other objects [@PhysRevD.51.3117; @*Virbhadra:1998dy; @*doi:10.1142/S021773230100398X; @*PhysRevD.65.103004; @*PhysRevD.74.024020; @*doi:10.1142/S0217732308025498; @*PhysRevD.77.124014]. In short, we can say that the possibility of having wormholes in our universe is a very important aspect of general relativity.

Wyman’s solution, also known as Fisher-Janis-Newman-Winicour solution, corresponds to the most general spherically symmetric solution to the Einstein–massless-scalar-field equations [@PhysRevD.24.839; @PhysRevD.86.084031]. It contains a particular case that can be seen as describing a spherical body and which is in agreement with the solar-system experiments [@PhysRevD.83.087502]. One also finds Wyman’s solution in the context of Brans-Dicke theory as a special case of the Campanelli-Lousto solutions [@PhysRevD.86.084031; @doi:10.1142/S0218271893000325; @PhysRevD.51.2011], in an alternative version of this theory 