Soliton Geometry of Modified Gravity Models Engaged with Strange Quark Matter Fluid and Penrose Singularity Theorem

The nature of the F(R,T)-gravity in conjunction with the quark matter fluid (QMF) is examined in this research note. In the F(R,T)-gravity framework, we derive the equation of state for the QMF in the form of: F(R,T)=F1(R)+F2(T) and the model of F(R)-gravity. We also discuss how the quark matter supports the Ricci solitons with a conformal vector field in F(R,T)-gravity. In this continuing work, we give estimates for the pressure and quark density in the phantom barrier period and the radiation epoch, respectively. Additionally, we use Ricci solitons to identify several black hole prospects and energy requirements for quark matter fluid spacetime (QMF-spacetime) connected with F(R,T)-gravity. Furthermore, in the F(R,T)-gravity model connected with QMF, we also discuss some applications of the Penrose singularity theorem in terms of Ricci solitons with a conformal vector field. Finally, we deduce the Schrödinger Equation using the equation of state of the F(R,T)-gravity model connected with QMF, and we uncover some constraints that imply the existence of compact quark stars of the Ia-supernova type in the QMF-spacetime with F(R,T)-gravity.