Global monopoles in Horndeski theory

In this article, global monopole solutions will be presented for the Horndeski theory by solving linearized field equations. We obtain two different classes of solutions depending on whether the Horndeski scalar field is massless or massive. Several properties of these solutions and the motion of test particles around them are discussed in detail, compared with the existing solutions in the literature. The mass due to an arbitrary potential of the scalar field changes the asymptotic behavior of the monopole compared to the massless case by applying a screening effect, which makes the monopole to asymptotically behave similarly to those in General Relativity. We also discussed the Galaxy rotation curves, and saw that only for the massless case and the massive case with very light scalar mass, the flattening of the galaxy rotation curves may be explained with global monopoles.