Mathematical Modeling Approach for Compact Objects: A New Metric Potential in the Spherically Symmetric System with Schwarzchild’s Coordinates

In this study, a new metric potential is created to generate exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions, so obtained, are very relevant to describe the compact stars like HerX-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Her~ X-1$$\end{document}, 4U1538-52\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4U1538-52$$\end{document}, SAXJ1808.4-3658\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SAX ~J1808.4-3658$$\end{document}, LMCX-4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$LMC~ X-4$$\end{document} and EXO1785-248\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EXO~ 1785-248$$\end{document}. These solutions are distinguished by the fact that they admit a linear equation of state which can be applied to strange stars with quark matter. In this model, we investigated various physical aspects such as energy density, pressure (both radial and transverse), anisotropy factor, mass, compactness parameter, surface redshift, and moment of inertia (approximate). Graphical methods were used to analyze energy conditions, equilibrium, and stability of the various of the compact stars and it has been deduced that our proposed model is applicable to anisotropic fluid spheres as all required conditions are fully satisfied. It is also worth mentioning that our model shows a monotonic reduction in the speed of sound with increasing radius.