Physical properties of class I compact star model for linear and Starobinsky−f(R,T) functions

Abstract We have explored exact solutions free from any physical and geometrical singularities, as well as the existence of compact stellar systems throughout linear and Starobinsky- f ( R , T ) − gravity theory. As we generally well-known, the general exact solutions of the altered Einstein Field Equations (EFEs) in the background of this gravity theory are one of the most complex tasks. To acquire simpler solution of the altered field equations, we consider linear and Starobinsky shape of the algebraic function as f ( R , T ) = R + 2 χ T and f ( R , T ) = R + ξ R 2 + 2 χ T (where R is scalar curvature, T is the trace of the stress–energy tensor and χ & ξ denotes a coupling constants). In this regards, we propose metric potentials e λ , and obtain the other metric potentials ( e ν ) under the embedding class one condition. We then compare the cases when ξ = χ = 0 [GR], ξ = 0 , χ = 0 . 5 [ f L ( R , T ) ], ξ = 0 . 5 , χ = 0 [ f S ( R , T ) ] and ξ = χ = 0 . 5 [ f S + L ( R , T ) ]. The obtained solution is well- behaved in all physical and mathematical points of view. Further, we provided a detailed physical acceptability of the solution by exploring main salient characteristics under different physical analysis in the linear f ( R , T ) − gravity. Moreover, the generalizing M − R and M − I curves from our solution are well fitted with observational data of the three compact objects viz., PSR J1614-2230, Vela X-1 and 4U 1820-30. We also found the beautiful results that the equation of state (EoS) is stiffest in χ = 0 than χ ≠ 0 , and the sensitivity in EoS is better in I − M graph than in M − R graph. Finally, we have successfully represented the effects of all the physical requirements in the arena of f ( R , T ) − gravity and we compared them with the standard GR results which can be recovered at χ = 0 .