The physically realizable anisotropic strange star models

In the present work, we search a new exact solution of Einstein’s field equations using Karmarkar condition of embedded class one space time. The new solution is analyzed graphically as well as analytically to check its viability for compact star modeling. The different parameters of the solution are ascertained by matching the interior space time metric with the Schwarzschild’s exterior space time metric. We tune our solution for the modeling of strange stars EXO1785-248, SAXJ1808.4-3658 and HER X-1 and found their masses and radii as 8.849 km, 1.3MΘ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{\Theta }$$\end{document} : 7.951 km, 0.9 MΘ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{\Theta }$$\end{document} : 8.1 km, 0.85MΘ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{\Theta }$$\end{document}, respectively. The physical reliability of the solution depends on the values of the independent parameters b and c. The solution is well behaved for the range of the values 0.000009≤b≤0.0039\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.000009\le b\le 0.0039$$\end{document} and 0.0000005≤c≤0.0000182\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.0000005\le c\le 0.0000182$$\end{document}. Our models satisfy the causality condition and adiabatic index is well behaved everywhere inside the fluid sphere. The compactness parameter is well defined as it does not cross the Buchdahl limit. All the energy conditions hold good inside the compact fluid spheres. The stability of models is assessed via Herrera’s cracking concept. The hydrostatic equilibrium condition is well maintained by our models as gravitational force is counterbalanced by the combined effects of anisotropic force and hydrostatic force. The proper graphical analysis is provided to authenticate the physically admissible character of proposed models.