Karmarkar Bardeen anisotropic model for compact stars in \(\mathcal{F}(\mathcal{R},\mathcal{T})\) gravity

This paper aims to obtain a new Class-I solution of the field equations in \(\mathcal{F}(\mathcal{R},\mathcal{T})\) gravitational theory for the charged anisotropic spherically symmetric distribution. For this purpose, a new spacetime metric function is put forth and employed in the Karmarkar condition. The uniform charge distribution in the stellar interior is considered and the Class-I spacetime is seamlessly matched to Bardeen geometry at the boundary. Moreover, a detailed analysis is conducted to study the physical attributes of the stars Vela X-1, SMC X-4, SAX J1808.4-3658, Her X-1 and Cen X-3, all obeying the essential conditions for a solution to be physically acceptable. A comprehensive review of stability criteria involving the energy conditions and adiabatic is provided complying with the requirement. In addition, an in-depth exploration of the Tolman-Oppenheimer-Volkoff’s (TOV) equation leads to the stellar configuration being in an equilibrium state.