Brans-Dicke Wormhole Revisited

TL;DR

This paper revisits the Brans-Dicke class I solution, deriving constraints for traversible wormholes, and discusses their physical plausibility and gravitational properties, including the presence of repulsive gravity at the throat.

Contribution

It provides a new constraint condition for Brans-Dicke wormholes and analyzes their physical viability and gravitational characteristics.

Findings

Wormholes satisfy a specific basic constraint for traversibility.

The solution may be analogous to a naked black hole.

Traversibility is only theoretical, not practical.

Abstract

A basic constraint to be satisfied by Brans class I solution for being a traversible wormhole is derived. It is argued that the solution could be a wormhole analogue of the Horowitz-Ross naked black hole. It is further demonstrated that the wormhole is traversible only "in principle", but not in practice. Using a recently proposed measure of total gravitational energy inside a static wormhole configuration, it is shown that the wormhole contains repulsive gravity required for the defocussing of orbits at the throat.