Slowly rotating wormholes: the first order approximation

We discuss a solution describing a rotating wormhole in the theory of gravity with a scalar field with negative kinetic energy. To solve the problem we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole's throat and the velocity of light. The rotating wormhole solution is constructed in the framework of the first order approximation with respect to the small parameter. We analyze the obtained solution and study the motion of test particles and the propagation of light in the spacetime of rotating wormhole.