Anisotropic compact stars in complexity formalism and isotropic stars made of anisotropic fluid under minimal geometric deformation (MGD) context in $$f(\mathscr {T})$$ f ( T ) gravity-theory

Abstract In this paper, we present an anisotropic solution for static and spherically symmetric self-gravitating systems by demanding the vanishing of the complexity factor (Herrera in Phys Rev D 97:044010, 2018) along with the isotropization technique through the gravitational decoupling (GD) approach (Ovalle in Phys Rev D 95:104019, 2017) in $$f(\mathscr {T})$$ f ( T ) -gravity theory. We begin by implementing gravitational decoupling via MGD scheme as the generating mechanism to obtain anisotropic solutions describing physically realizable static, spherical self-gravitating systems. We adopt the Krori–Barua ansatz and present two new classes of stellar solutions: the minimally deformed anisotropic solution with a vanishing complexity factor and the isotropic solution via gravitational decoupling. We demonstrate that both classes of solutions obey conditions of regularity, causality and stability. An interesting feature is the switch in trends of some of the thermodynamical quantities such as effective density, radial and transverse stresses at some finite radius, $$r=r_*$$ r = r ∗ , depending on different values of the decoupling constant $$\beta $$ β . We show that gravitational decoupling via the vanishing complexity factor enhances the stability of the stellar fluid surrounding the core’s central areas. By analyzing the effect of the decoupling constant $$\beta $$ β on the $$M-Y_{TF}$$ M - Y TF plots, (where $$Y_{TF}$$ Y TF denotes the complexity factor) derived from both solutions, we find that a small contribution from the complexity factor leads to the prediction of lower maximum mass of a self-gravitating compact star via gravitational decoupling in $$f(\mathscr {T})$$ f ( T ) -gravity compared to their pure $$f(\mathscr {T})$$ f ( T ) -gravity counterparts. Furthermore, we have also determined the impact of decoupling constant $$\beta $$ β and surface density on predicted radii via $$M{-}R$$ M - R for some known compact objects.