Solutions of the Einstein–Maxwell equations with energy–momentum tensor for polytropic core and linear envelope

Abstract Investigating an anisotropic charged spherically symmetric core-envelope model for dense star objects is the aim of this paper. The polytropic equation of state (EoS) defines the core of this model, while the linear EoS represents the envelope. The radiation density-containing energy–momentum tensor is used to determine the solution of the Einstein–Maxwell field equations. All three regions-core, envelope, and Reissner Nordström external metric-have perfect matching. For the intrinsic structure of the stars $$SAX~J1808.4-3658$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>A</mml:mi> <mml:mi>X</mml:mi> <mml:mspace/> <mml:mi>J</mml:mi> <mml:mn>1808.4</mml:mn> <mml:mo>-</mml:mo> <mml:mn>3658</mml:mn> </mml:mrow> </mml:math> and $$4U1608-52$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>U</mml:mi> <mml:mn>1608</mml:mn> <mml:mo>-</mml:mo> <mml:mn>52</mml:mn> </mml:mrow> </mml:math> , the model is physically feasible. Additionally, the Tolman–Oppenheimer–Volkoff (TOV) equation is used to verify the equilibrium state, and the adiabatic index is used to verify stability.