Expanding ($n+1$)-dimensional wormhole solutions in Brans-Dicke cosmology

We have obtained two classes of ($n+1$)-dimensional wormhole solutions using a traceless energy-momentum tensor in the Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry, while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric space-time also appear among the solutions as special cases. We have also considered the traversability of the wormhole solutions and have shown that they are indeed traversable. Finally, we have discussed the energy-momentum tensor which supports this geometry and have checked for the energy conditions. We have found that wormhole solutions in the first class of solutions violate the weak energy condition (WEC). In the second class, the wormhole geometries in a closed universe do violate the WEC, but in an open universe with a suitable choice of constants the supporting matter energy-momentum tensor can satisfy the WEC. However, even in this case the full effective energy-momentum tensor including the scalar field and the matter energy-momentum tensor still violates the WEC.

Figure 1

The behavior of $1+a(r)$ and $d(r)$ for different choices of constants.

Figure 2

The behavior of $1+a(r)$ and $d(r)$ for different choices of constants.

Figure 3

The energy condition factors are plotted against $r$. The first three plots are for a wormhole in an open universe. Figure 3d corresponds to $\rho +P_t$ for a wormhole in a closed universe.