Exact wormhole solutions with nonminimal kinetic coupling and the cosmological constant

We consider scalar-tensor theory of gravity with the cosmological constant and a scalar field possessing the nonminimal kinetic coupling to the curvature. The Lagrangian of the theory contains the term (𝜀𝑔𝜇𝜈+𝜂𝐺𝑖𝑗)𝜑,𝑖𝜑,𝑗 and represents a particular case of the general Horndeski Lagrangian, which leads to second-order equations of motion. We found a class of exact particular static spherically symmetric solutions describing wormholes with nonminimal kinetic coupling. It is shown that wormholes with canonical scalar field (𝜀 = +1) exist in case of the negative cosmological constant. The wormhole throat connects two anti-de Sitter spacetimes.