Exploring decoupling process and energy exchange in compact stars induced by dark matter spike density profile within complexity free domain

Abstract This study focuses on the characteristics of compact stars composed of dark matter induced by gravitational decoupling in the context of the general theory of relativity. We are proposing an anisotropic model holding an Einasto spike dark matter density profile. The vanishing complexity factor along with a complete geometric deformation approach has been used to solve the decoupled field equations for the spherically symmetric celestial objects. In the current decoupled solution, the decoupling parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> determines the quantity of dark matter content inside the object. Additionally, we determine the model’s physical quantities such as pressure, density, anisotropy, causality criteria, energy exchange between the fluid distributions, and variation of mass with central density mass within the stellar model PSR J0952-0607 for different values of $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> which shows the impact of dark matter content on these physical quantities. Furthermore, we have also shown the influence of $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> on the radii of the astrophysical binary pulsars GW190814, PSR J0952-0607, and PSR J1614-2230. In the framework of the decoupling approach, our graphical findings show that binary pulsars have mass lower than $$M_{max}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> but higher radii for a specific $$M{-}R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>-</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> curve for well-defined values of given parameters.