Gravitational decoupling of anisotropic stars in the Brans–Dicke theory

Abstract

Abstract Anisotropic spherically symmetric solutions within the framework of the Brans–Dicke theory are uncovered through a unique gravitational decoupling approach involving a minimal geometric transformation. This transformation effectively divides the Einstein field equations into two separate systems, resulting in the alteration of the radial metric component. The first system encompasses the influence of the seed source, derived from the metric functions of the isotropic Tolman IV solution. Meanwhile, the anisotropic source is subjected to two specific constraints in order to address the second system. By employing matching conditions to determine the unknown constants at the boundary of the stellar object, a comprehensive examination of the internal structure of stellar systems ensues. This investigation delves into the impact of the decoupling parameter, the Brans–Dicke parameters, and a scalar field on the structural characteristics of anisotropic spherically symmetric spacetimes, all while considering the strong energy conditions.