Eur. Phys. J. C (2019) 79: 885
https://doi.org/10.1140/epjc/s10052-019-7366-3

Regular Article - Theoretical Physics

Anisotropic relativistic fluid spheres: an embedding class I approach

¹ Departamento de Física, Facultad de ciencias básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile
² Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Nizwa, Sultanate of Oman
³ Laboratory of High Energy Physics and Condensed Matter (LPHEMaC), Department of Physics, Faculty of Sciences Aïn Chock, University of Hassan II, Mâarif, B.P. 5366, 20100, Casablanca, Morocco
⁴ Department of Physics, National Defence Academy, Khadakwasla, Pune, 411023, India
⁵ Department of Physics, Faculty of Sciences, University of Ibn Tofail, B.P. 133, 14000, Kenitra, Morocco
⁶ Abdus Salam International Centre for Theoretical Physics, Miramare, Trieste, Italy

^* e-mail: francisco.tello@ua.cl

Received: 13 July 2019
Accepted: 1 October 2019
Published online: 31 October 2019

Abstract

In this work, we present a new class of analytic and well-behaved solution to Einstein’s field equations describing anisotropic matter distribution. It’s achieved in the embedding class one spacetime framework using Karmarkar’s condition. We perform our analysis by proposing a new metric potential which yields us a physically viable performance of all physical variables. The obtained model is representing the physical features of the solution in detail, analytically as well as graphically for strange star candidate SAX J1808.4-3658 (,  km), with different values of parameter n ranging from 0.5 to 3.4. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, Abreu’s criterion and relativistic adiabatic index , and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable. The physical sensitivity of the moment of inertia (I) obtained from the solutions is confirmed by the Bejger−Haensel concept, which could provide a precise tool to the matching rigidity of the state equation due to different values of n viz., and 3.4.