Most general isotropic charged fluid solution for Buchdahl model in $\mathscr{F}(Q)$ gravity

Abstract: In this work, we investigated a most general isotropic charged fluid solution for the Buchdahl model via a two-step method in $\mathscr{F}(Q)$-gravity framework for the first time. In this context, a linear function of the form $\mathscr{F}(Q)=\zeta_1 Q+\zeta_2$ and a particular transformation is used to solve the Einstein-Maxwell Equations (EMEs) employing the Buchdahl ansatz: $ e^{\Upsilon(r)}=\frac{\mu(1+\lambda r^2)}{\mu+\lambda r^2}$, where $\zeta_1$, $\zeta_2$, $\lambda$ and $\mu$ are constant parameters. The Schwarzschild de Sitter~(AdS) exterior solution is joined to the interior solution at the boundary to determine the constant parameters. It should be emphasized that, for a given transformation, the Buchdahl ansatz only offers a mathematically feasible solution in the context of electric charge, where pressure and density are maximum at the center and decrease monotonically towards the boundary when $0<\mu<1$. We taken into account the compact star EX01785-248 with $M=(1.3\pm 0.2)M_{\odot}$; Radius $=12.02^{+0.55}_{-0.55}$~km for graphical analysis. The physical acceptability of the model in the context of $\mathscr{F}(Q)$ has been evaluated by looking at the necessary physical properties, including energy conditions, causality, hydrostatic equilibrium, pressure-density ratio, etc. Additionally, we predicted the maximum mass limit of different compact objects for various parameter values along with the mass-radius relation. The maximum masses range (1.927 - 2.321)~$M_\odot$ are obtained for our solution. It can be observed that when the coupling parameter $\zeta_1$ for $\mathscr{F}(Q)$ gravity is smaller, then our solution yields massive stars. The present investigation provides novel insights and realistic implications regarding the formation of compact astrophysical objects.