Notes on wormhole existence in scalar-tensor and F(R) gravity

TL;DR

This paper critically examines claims of wormhole solutions in scalar-tensor and F(R) gravity, showing that such solutions are either not true wormholes or involve negative effective gravity, indicating ghost degrees of freedom.

Contribution

It clarifies the conditions under which wormhole solutions in scalar-tensor and F(R) gravity are physically viable, highlighting the necessity of positive effective gravity for true wormholes.

Findings

No vacuum wormholes in Brans-Dicke theory with a > -3/2 except at a=0

Wormhole solutions require F(R) to have an extremum where G_eff changes sign

Effective gravitational constant G_eff is negative in regions of some solutions

Abstract

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G_eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant \omega > -3/2, except for the case \omega = 0; in the latter case, G_eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G_eff changes its sign.