Study of compact stars in $${\mathcal {R}}+ \alpha {\mathcal {A}}$$ gravity

Abstract

AbstractThe main goal of this work is to provide a comprehensive study of relativistic structures in the context of recently proposed $${\mathcal {R}}+ \alpha {\mathcal {A}}$$ R + α A gravity, where $${\mathcal {R}}$$ R is the Ricci scalar, and $${\mathcal {A}}$$ 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 $${\mathcal {R}}+ \alpha {\mathcal {A}}$$ 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 $$g_{rr}$$ g rr and $$g_{tt}$$ 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 $$4U~1538{-}52$$ 4 U 1538 - 52 , $$SAX~J1808.4{-}3658$$ S A X J 1808.4 - 3658 , $$Her~X{-}1$$ H e r X - 1 , $$LMC~X{-}4$$ L M C X - 4 , $$SMC~X{-}4$$ S M C X - 4 , $$4U~1820{-}30$$ 4 U 1820 - 30 , $$Cen~X{-}3$$ C e n X - 3 , $$4U~1608{-}52$$ 4 U 1608 - 52 , $$PSR~J1903{+}327$$ P S R J 1903 + 327 , $$PSR~J1614{-}2230$$ P S R J 1614 - 2230 , $$Vela~X{-}1$$ V e l a X - 1 , $$EXO~1785{-}248$$ E X O 1785 - 248 . To evaluate the feasibility of $${\mathcal {R}}+ \alpha {\mathcal {A}}$$ 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 $${\mathcal {R}}+ \alpha {\mathcal {A}}$$ R + α A gravity supports the existence of compact objects which follow observable patterns.