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arXiv · 1408.1235

Exact wormhole solutions with nonminimal kinetic coupling

R. V. Korolev·Sergey V. Sushkov
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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 $(\varepsilon g^{μν}+ηG^{μν})ϕ_{,μ}ϕ_{,ν}$ 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 $η>0$. 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.

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R. V. Korolev, Sergey V. Sushkov. 2014-08-06. Exact wormhole solutions with nonminimal kinetic coupling. https://doi.org/10.1103/physrevd.90.124025

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