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In this paper, we discuss asymptotically flat and anti-de Sitter (AdS) boson star in    $$(4+1)$$  ( 4 + 1 ) -dimensional Gauss–Bonnet gravity. We describe the dependence of the mass, the charge and the radius of the boson star on the model parameters, such as Gauss–Bonnet coupling    $$\alpha $$  α , cosmological constant    $$\Lambda $$  Λ and gravitational constant    $$\kappa $$  κ . The basic properties of the solutions of boson stars have been studied for the different negative values of Gauss–Bonnet coupling. We found that when    $$\kappa $$  κ is large and    $$\alpha $$  α is negative enough, the spiral shrinks and pulls back to the larger internal frequency    $$\omega $$  ω , and there is only one branch exists. We have also observed that when    $$\kappa $$  κ is small enough and if    $$\alpha $$  α is close to zero, the spiral will unfold.

Boson stars with negative Gauss–Bonnet coupling