Expanding $(n+1)$-Dimensional Wormhole Solutions in Brans-Dicke Cosmology

TL;DR

This paper presents new higher-dimensional wormhole solutions in Brans-Dicke gravity, analyzing their geometry, traversability, and energy conditions, revealing cases where the weak energy condition can be satisfied.

Contribution

The study introduces two classes of $(n+1)$-dimensional wormhole solutions in Brans-Dicke theory, exploring their properties and energy condition violations.

Findings

Wormhole solutions in open and closed universes were obtained.

Some solutions can satisfy the weak energy condition under specific parameters.

All solutions violate the weak energy condition when considering the full scalar and matter fields.

Abstract

We have obtained two classes of $(n+1)$-dimensional wormhole solutions using a traceless energy-momentum tensor in 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 spacetime also appear among the solutions as special cases. We have also considered the travesibility of the wormhole solutions and have shown that they are indeed traverseable. 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 weak energy condition (WEC). In the second class, the wormhole geometries in a closed universe do violate WEC, but in an open universe with suitable choice of constants the supporting matter energy-momentum tensor can satisfy 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.