Most general exact solution for charged compact star model in extended symmetric teleparallel gravity using two step-method

Abstract

This article investigates the physical properties and stability of an isotropic compact star in $F\left(Q,T\right)$ gravity, where $T$ denotes the trace of the energy-momentum tensor and $Q$ represents the nonmetricity scalar. In the present study, the impact of $F\left(Q,T\right)$ gravity on the stability and structure of compact stars is investigated, considering a perfect fluid distribution and adopting the functional form $F\left(Q,T\right)={\xi }_{1}Q+{\xi }_{2}T$. The field equations are solved using the two-step method proposed by Gupta and Jasim [Astrophys. Space Sci. 283 (2003) 337], along with the Buchdahl ansatz given by $e^{\phi }=\frac{\Upsilon (1+ϵr^2)}{\Upsilon +ϵr^2}$. To investigate the physical properties of the LMC X-4 compact star, a static spherically symmetric metric is employed in the interior region, while a Reissner-Nordstrom exterior metric is adopted for the exterior region. In the interior region of the proposed stellar object, we analyze the behaviour of the spacetime metric functions ($e^{\phi }$ and $e^{\vartheta }$), energy density (ρ), pressure (P), charge (q), ratio of pressure to density (Ω) and the energy conditions. The equilibrium state of the star is analysed using the Tolman-Oppenheimer-Volkoff (TOV) equation, expressed as $F_G+F_H+F_{(Q,T)}+F_Q=0$. To assess the stability of the configuration, we examine the adiabatic index (Γ), the causality condition, regularity conditions, the well-behaved condition and the stability against convection criterion.