Physical characteristics of anisotropic solutions in f(Q,T) gravity under the vanishing complexity, embedding class one, conformally flat and conformally Killing conditions

The foundation of this paper is to present a comparative study of the properties of anisotropic solutions for compact stars in the framework of modified $f(Q,T)$ gravity for the first time under the schemes of vanishing complexity, embedding class one, conformally flat and conformally Killing, where Q is the nonmetricity scalar and T is the trace of the energy-momentum tensor. The model $f(Q,T)=\varphi Q+\alpha Q^{n+1}-\gamma (1-e^{-Q/\gamma })+\beta T$ is chosen in order to compare the results of the various forms $f(Q,T)$ and $f\left(Q\right)$ gravity theories. The $f(Q,T)$ and $f\left(Q\right)$ gravities in this model are then further simplified to depend on parameters $\varphi ,\alpha ,\gamma \&\beta$. Then, we discussed several approaches to determining the spherically symmetric spacetime components. Schwarzschild geometry represents the exterior spacetime, while a Tolman-Kuchowiz spacetime is used to examine the spherically symmetric spacetime inside the interior geometry. Many properties of compact stars are investigated, like energy density, energy conditions, pressure profiles, sound speeds, gradients, adiabatic index, TOV equation, mass function, compactness, and redshift function are all carefully examined in order to complete the analysis. We have compiled results for both stable and unstable scenarios, derived from gravity theories categorized into various cases, with solutions considered under different frameworks such as Tolman-Kuchowiz spacetime, embedding class 1 spacetime, the vanishing complexity condition, the conformally flat condition, and the conformal Killing vector condition.