Complexity-free solution generated by gravitational decoupling for anisotropic self-gravitating star in symmetric teleparallel f(Q)-gravity theory

Abstract

In this work, we attempt to find an anisotropic solution for a compact star generated by gravitational decoupling in f(Q)-gravity theory having a null complexity factor. To do this, we initially derive the complexity factor condition in f(Q) gravity theory using the definition given by Herrera (Phys Rev D 97:044010, 2018) and then derived a bridge equation between gravitational potentials by assuming complexity factor to be zero (Contreras and Stuchlik in Eur Phys J C 82:706, 2022). Next, we obtain two systems of equations using the complete geometric deformation (CGD) approach. The first system of equations is assumed to be an isotropic system in f(Q)-gravity whose isotropic condition is similar to GR while the second system is dependent on deformation functions. The solution of the first system is obtained by Buchdahl’s spacetime geometry while the governing equations for the second system are solved through the mimic constraint approach along with vanishing complexity condition. The novelty of our work is to generalize the perfect fluid solution into an anisotropic domain in f(Q)-gravity theory with zero complexity for the first time. We present the solution’s analysis to test its physical viability. We exhibit that the existence of pressure anisotropy due to gravitational within the self-gravitating bounded object plays a vital role to stabilize the f(Q) gravity system. In addition, we show that the constant involved in the solution controls the direction of energy flow between the perfect fluid and generic fluid matter distributions.