# Compact star models in class I spacetime

Sarkar, Nayan (Aff1, 0000 0001 0722 3459, grid.216499.1, Department of Mathematics, Jadavpur University, 700032, Kolkata, India) ; Singh, Ksh. Newton (Aff2, 0000 0001 0722 3459, grid.216499.1, Faculty Council of Science, Jadavpur University, 700032, Kolkata, India) (Aff3, 0000 0001 2373 2499, grid.464969.0, Department of Physics, National Defence Academy, Khadakwasla, 411023, Pune, India) ; Sarkar, Susmita (Aff1, 0000 0001 0722 3459, grid.216499.1, Department of Mathematics, Jadavpur University, 700032, Kolkata, India) ; Rahaman, Farook (Aff1, 0000 0001 0722 3459, grid.216499.1, Department of Mathematics, Jadavpur University, 700032, Kolkata, India)

17 June 2019

Abstract: In the present article, we have presented completely new exact, finite and regular class I solutions of Einstein’s field equations i.e. the solutions satisfy the Karmarkar condition. For this purpose needfully we have introduced a completely new suitable 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} metric potential to generate the model. We have investigated the various physical aspects for our model such as energy density, pressure, anisotropy, energy conditions, equilibrium, stability, mass, surface and gravitational red-shifts, compactness parameter and their graphical representations. All these physical aspects have ensured that our proposed solutions are well-behaved and hence represent physically acceptable models for anisotropic fluid spheres. The models have satisfied causality and energy conditions. The presented models are also stable by satisfying Bondi condition and Abreu et al. condition, in equilibrium position and static by satisfying TOV equation, Harrison–Zeldovich–Novikov condition, respectively. For the parameters chosen in the paper are matching in modeling Vela X-1, Cen X-3, EXO 1785-248 and LMC X-4. The M – R graph generated from the solutions is matching the ranges of masses and radii for the considered compact stars. This work also estimated the approximate moment of inertia for the mentioned compact stars.

Published in: EPJC 79 (2019) 516 DOI: 10.1140/epjc/s10052-019-7035-6