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

TL;DR

This paper derives a new isotropic charged fluid solution within $ abla$-gravity for compact stars, analyzing physical properties and maximum mass limits, revealing that smaller coupling parameters lead to more massive stars.

Contribution

It presents the first general isotropic charged fluid solution for the Buchdahl model in $ abla$-gravity, incorporating a linear $ abla(Q)$ function and boundary matching with Schwarzschild de Sitter exterior.

Findings

Maximum mass range of 1.927 to 2.321 solar masses for different parameters.

Solution yields more massive stars with smaller coupling parameter $ abla_1$.

Model satisfies physical conditions like energy, causality, and hydrostatic equilibrium.

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.