Study of a Minimally Deformed Anisotropic Solution for Compact Objects with Massive Scalar Field in Brans–Dicke Gravity Admitting the Karmarkar Condition

Abstract

In the present paper, we focused on exploring the possibility of providing a new class of exact solutions for viable anisotropic stellar systems by means of the massive Brans–Dicke (BD) theory of gravity. In this respect, we used the decoupling of gravitational sources by minimal geometric deformation (MGD) (e−η=Ψ+βh) for compact stellar objects in the realm of embedding class-one space-time to study anisotropic solutions for matter sources through the modified Einstein field equations. For this purpose, we used the ansatz for Ψ relating to the prominent, well-known and well-behaved Finch–Skea model via Karmarkar condition, and the determination scheme for deformation function h(r) was proposed via mimic requirement on radial pressure component: θ11(r)=pr(r) and matter density: θ00(r)=ρ(r) for the anisotropic sector. Moreover, we analyzed the main physical highlights of the anisotropic celestial object by executing several physical tests for the case θ11(r)=pr(r). We have clearly shown how the parameters α, β and ωBD introduced by massive BD gravity via the MGD approach incorporating the anisotropic profile of the matter distribution have an immense effect on many physical parameters of compact bodies such as LMC X-4, LMC X-4, Her X-1, 4U 1820-30, 4U 1608-52, SAX J1808.4–658 and many others that can be fitted.