Anisotropic compact stellar model of embedding class-I satisfying Karmarkar’s condition in Vaidya and Tikekar spheroidal geometry

We present a class of solutions for a spherically symmetric anisotropic matter distribution in Vaidya and Tikekar spheroidal geometry. Making use of the Vaidya and Tikekar (VT) metric ansatz (J Astrophys Astron 3:325, 1982) for one of the metric functions grr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{rr}$$\end{document}, we obtain the unknown metric function gtt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{tt}$$\end{document} by utilizing the Karmakar’s embedding condition which makes the master equation tractable. The model parameters are fixed by utilizing the matching conditions of the interior spacetime and the exterior Schwarzschild solution at the boundary of the star where the radial pressure vanishes. The closed-form interior solution of the Einstein field equations thus obtained is shown to be capable of describing ultra-compact stellar objects where anisotropy might develop. The current estimated masses and radii of some other pulsars are utilized to show that the developed model meets all the requirements of a realistic star. The stability of the model is analyzed. The dependence of the curvature parameter K of the VT model, which characterizes a departure from homogeneous spherical distribution, is also investigated.