Role of vanishing complexity factor in generating spherically symmetric gravitationally decoupled solution for self-gravitating compact object

In this work, we study the role of the vanishing complexity factor in generating self-gravitating compact objects under gravitational decoupling technique in f ( Q )-gravity theory. To tackle the problem, the gravitationally decoupled action for modified f ( Q ) gravity has been adopted in the form

$${\mathscr {S}}={{\mathscr {S}}_{Q}}+{{\mathscr {S}}^{*}_{\theta }}$$

S = S Q + S θ ∗ , where

$${\mathscr {S}}_Q$$

S Q denotes the Lagrangian density of the fields which appears in the f ( Q ) theory while

$${\mathscr {S}}^{*}_{\theta } (=\alpha {\mathscr {S}}_{\theta }$$

S θ ∗ ( = α S θ , where

$$\alpha$$

α is just a coupling parameter which controls the deformation) describes the Lagrangian density for a new kind of gravitational sector which has not been included in f ( Q ) gravity. After that, we developed an important relation between gravitational potentials via a systematic approach (Contreras and Stuchlik in Eur Phys J C 82:706, 2022) using the vanishing complexity factor condition in the context of f ( Q ) theory. We have used the Buchdahl model along with the mimic-to-density constraints approach for generating the complexity-free anisotropic solution. The qualitative physical analysis has been done along with the mass-radius relation for different compact objects via

$$M-R$$

M - R curves to validate our solution. It is noticed that the coupling constant

$$\beta _1$$

β 1 has a definite impact on constraining the mass and radii of the object that are shown in

$$M-R$$

M - R curves. The obtained results show that the compactness of the objects can be controlled by the coupling parameters.