Exact solutions of Brans-Dicke wormholes in the presence of matter

TL;DR

This paper derives exact wormhole solutions in Brans-Dicke theory where ordinary matter obeys energy conditions, attributing exotic features to the scalar field's effective stress-energy tensor, thus reducing the need for exotic matter.

Contribution

It presents new exact wormhole solutions in Brans-Dicke theory with matter satisfying null energy conditions, highlighting the scalar field's role in sustaining the wormhole geometry.

Findings

Normal matter satisfies null energy condition

Scalar field acts as effective exotic matter

Solution requires matching to an exterior vacuum

Abstract

A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition. Although a plethora of wormhole solutions have been explored in the literature, it is useful to find geometries that minimize the usage of exotic matter. In this work, we find exact wormhole solutions in Brans-Dicke theory where the normal matter threading the wormhole satisfies the null energy condition throughout the geometry. Thus, the latter implies that it is the effective stress-energy tensor containing the scalar field, that plays the role of exotic matter, that is responsible for sustaining the wormhole geometry. More specifically, we consider a zero redshift function and a particular choice for the scalar field and determine the remaining quantities, namely, the stress-energy tensor components and the shape function. The solution found is not asymptotically flat, so that this interior wormhole spacetime needs to be matched to an exterior vacuum solution.