Brans-Dicke cylindrical wormholes

Static axisymmetric thin-shell wormholes are constructed within the framework of the Brans-Dicke scalar-tensor theory of gravity. Examples of wormholes associated with vacuum and electromagnetic fields are studied. All constructions must be threaded by exotic matter, except in the case of geometries with a singularity of finite radius, associated with an electric field, which can have a throat supported by ordinary matter. These results are achieved with any of the two definitions of the flare-out condition considered.

Figure 1

Geometries with a radial electric field: The regions where $a>r_s$ (dark gray) and $a<r_s$ (light gray) are shown in terms of the parameters $d$ and $n$, for different values of the Brans-Dicke constant $\omega$. White zones are nonphysical, since they correspond to values such that the throat radius is not real and positive. The upper row corresponds to values of the Brans-Dicke constant for which the field is a ghost, while the lower row corresponds to normal fields.

Figure 2

Geometries with a radial electric field: The gray zones correspond to values of the parameters such that the energy conditions are satisfied when the radial flare-out condition is adopted. The upper row corresponds to values of the Brans-Dicke constant for which the field is a ghost, while the lower row corresponds to normal fields.

Figure 3

Geometries with a radial electric field: The gray zones correspond to values of the parameters such that the energy conditions are satisfied when the areal flare-out condition is adopted. The upper row corresponds to values of the Brans-Dicke constant for which the field is a ghost, while the lower row corresponds to normal fields.