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 $(\epsilon g^{\mu \nu }+\eta G^{\mu \nu }){\varphi }_{,\mu }{\varphi }_{,\nu }$ 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 $\epsilon =-1$ (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.

7 pages, 3 figures, to be submitted to PRD

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• More about stable wormholes in beyond Horndeski theory
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• General constraints on Horndeski wormhole throats
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• Giant wormholes in ghost-free bigravity theory
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• Self-Gravitating Static Non-Critical Black Holes in 4$D$ Einstein-Klein-Gordon System with Nonminimal Derivative Coupling