Brans-Dicke Wormhole Revisited -- II

TL;DR

This paper revisits Brans-Dicke wormholes, showing how to obtain regular, singularity-free solutions in a new parameter range, and clarifies the conditions under which wormholes can exist in scalar-tensor theories.

Contribution

It demonstrates a method to generate regular wormhole solutions in Brans-Dicke theory outside previously known parameter ranges, expanding understanding of wormhole existence conditions.

Findings

Regular, singularity-free wormholes are possible for -2<ω<-3/2.

A new wormhole solution with two asymptotically flat regions is constructed.

The parameter range for non-singular wormholes is revised and clarified.

Abstract

In a recent paper [arXiv:0910.1109], a wormhole range in the Jordan frame, -3/2<{\omega}<-4/3 for the vacuum Brans-Dicke Class I solution was derived. On general grounds and under certain conditions, it is shown in a theorem that static wormhole solutions in the scalar-tensor theory are not possible. We agree with the conclusion within its framework but report that a singularity-free wormhole can be obtained from Class I solution by performing certain operations on it, a fact possibly not yet widely known. The transformed solution is regular everywhere, produces a wormhole with two asymtotically flat regions for a revised new range -2<{\omega}<-3/2, together with a wormhole analogue (of Horowitz-Ross naked black hole) that we discovered earlier. This new range lies in the ghost regime in the Einstein frame consistent with the theorem. We further conclude that there is a fixed point at {\omega}=-3/2, the values {\omega}>-3/2 correspond to singular wormholes, while values {\omega}<-3/2 correspond to singularity-free wormholes.