A Nonsingular Brans Wormhole: An Analogue to Naked Black Holes

TL;DR

This paper constructs a non-singular wormhole solution in Brans-Dicke theory, serving as an analogue to naked black holes, by transforming a known solution and analyzing its properties within a specific parameter range.

Contribution

It introduces a Wick-rotated, singularity-free wormhole solution in Brans-Dicke theory, expanding the understanding of wormhole analogues to naked black holes.

Findings

A non-singular wormhole solution is obtained via Wick rotation of Class I solution.

The new solution exists in the parameter range -2<ω<-3/2.

The maximum tidal forces occur above the throat, similar to naked black holes.

Abstract

In a recent paper, we showed the Jordan frame vacuum Brans Class I solution provided a wormhole analogue to Horowitz-Ross naked black hole in the wormhole range -3/2<{\omega}<-4/3. Thereafter, the solution has been criticized by some authors that, because of the presence of singularity in that solution within this range, a wormhole interpretation of it is untenable. While the criticism is correct, we show here that (i) a singularity-free wormhole can actually be obtained from Class I solution by performing a kind of Wick rotation on it, resulting into what Brans listed as his independent Class II solution (ii) the Class II solution has all the necessary properties of a regular wormhole in a revised range -2<{\omega}<-3/2 and finally, (iii) naked black holes, as described by Horowitz and Ross, are spacetimes where the tidal forces attain their maxima above the black hole horizon. We show that in the non-singular Class II spacetime this maxima is attained above the throat and thus can be treated as a wormhole analogue. Some related issues are also addressed.