Boson stars in non-minimal gravity

Abstract We study the boson star solutions in a theory involving a complex scalar field in a conical scalar field potential: V ( | Φ | ) := 2 λ | Φ | in the presence of non-minimal gravity given by the term: ( ξ R | Φ | 2 ) in the action, where ξ is a constant parameter that couples the complex scalar field Φ with the Ricci scalar R and is treated, in our work, as a free parameter. The theory has one more free parameter denoted by α := 8 π G λ 2 / ω 4 (where ω is the frequency of the complex scalar field). Here G is the Newton’s gravitational constant, λ is a constant used in the definition of the scalar field potential. We find that the acceptable boson star solutions exist in this theory that involves non-minimal gravity as above. For obtaining the acceptable boson star solutions, we obtain the domain of existence of our free parameters ξ and α for which the boson star solutions exist and then study the various properties of the boson star solutions. In our studies, as we trace the evolution of our solutions along the relevant path, emanating from the solutions corresponding to the absence of gravitational field, we observe a steady increase in mass with radius. Employing principles from catastrophe theory, we find that this trajectory remains stable until it reaches the maximum mass value. This leads to the characteristic spiraling behavior of the mass-radius curve, a well-known feature in compact star models signaling the onset of instability.