Exact wormhole solutions with nonminimal kinetic coupling

TL;DR

This paper derives exact static spherically symmetric wormhole solutions in a scalar-tensor gravity theory with nonminimal kinetic coupling, showing they exist under specific conditions and connect two anti-de Sitter spacetimes without curvature singularities.

Contribution

It provides the first analytical wormhole solutions in a scalar-tensor theory with nonminimal kinetic coupling, expanding the understanding of possible wormhole geometries.

Findings

Wormholes exist only for phantom scalar fields with positive coupling.

The wormhole connects two anti-de Sitter spacetimes.

No curvature singularities are present at the wormhole throat.

Abstract

We consider static spherically symmetric solutions in the scalar-tensor theory of gravity with a scalar field possessing the nonminimal kinetic coupling to the curvature. The lagrangian of the theory contains the term $(\varepsilon g^{\mu\nu}+\eta G^{\mu \nu})\phi_{,\mu}\phi_{,\nu}$ and represents a particular case of the general Horndeski lagrangian, which leads to second-order equations of motion. We use the Rinaldi approach to construct analytical solutions describing wormholes with nonminimal kinetic coupling. It is shown that wormholes exist only if $\varepsilon=-1$ (phantom case) and $\eta>0$. The wormhole throat connects two anti-de Sitter spacetimes. The wormhole metric has a coordinate singularity at the throat. However, since all curvature invariants are regular, there is no curvature singularity there.