Exact wormhole solutions with nonminimal kinetic coupling

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 $(ϵ{g}^{\ensuremath{\mu}\ensuremath{\nu}}+\ensuremath{\eta}{G}^{\ensuremath{\mu}\ensuremath{\nu}}){\ensuremath{\phi}}_{,\ensuremath{\mu}}{\ensuremath{\phi}}_{,\ensuremath{\nu}}$ 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 $ϵ=\ensuremath{-}1$ (phantom case) and $\ensuremath{\eta}g0$. 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.