Study of compact stars in $R$ + α$A$ gravity

The main goal of this work is to provide a comprehensive study of relativistic structures in the context of recently proposed $R$ + α$A$ gravity, where $R$ is the Ricci scalar, and $A$ is the anti-curvature scalar. For this purpose, we examine a new classification of embedded class-I solutions of compact stars. To accomplish this goal, we consider an anisotropic matter distribution for $R$ + α$A$ gravity model with static spherically symmetric spacetime distribution. Due to highly non-linear nature of field equations, we use the Karmarkar condition to link the g${}_{rr}$ and g${}_{tt}$ components of the metric. Further, we compute the values of constant parameters using the observational data of different compact stars. It is worthy to mention here that we choose a set of twelve important compact stars from the recent literature namely 4U 1538-52, SAX J1808.4-3658, Her X-1, LMC X-4, SMC X-4, 4U 1820-30, Cen X-3, 4U 1608-52, PSR J1903+327, PSR J1614-2230, Vela X-1, EXO 1785-248. To evaluate the feasibility of $R$ + α$A$ gravity model, we conduct several physical checks, such as evolution of energy density and pressure components, stability and equilibrium conditions, energy bounds, behavior of mass function and adiabatic index. It is concluded that $R$ + α$A$ gravity supports the existence of compact objects which follow observable patterns.