Journal of Physics Research and Education, Vol.1, No.1, January 2021 123 Relativistic compact stellar model describing anisotropic stars Lipi Baskey• Department of Mathematics, Govt. General Degree College at Kushmandi, Dakshin Dinajpur, West Bengal, 733 121, India. Shyam Dast Department of Physics, P. D. Womens' College, Jalpaiguri, West Bengal, 735101, India. (Dated: March 18, 2020) In this paper, we have derived a class of analytical solutions of Einstein fi eld equations for a spherically symmetric anisotropic matter distribution. By choosing one of the metric potentials grr to be Krori-Barua metric type and a specific choice of anisotropy we obtain the other metric function. The interior solutions thus obtained has been utilized to construct a potentially stable model that could describe compact ste llar objects. The exterior vacuum region has been assigned with the Schwarzschild spacet ime metric. Across the boundary of the compact star where t he radial pressure drops to zero, the interior metric has been matched smoothly with the exterior metric to fix the model parameters associated with the solutions. All the regularity conditions, energy conditions and all other physical requirements demanded for a realistic compa ct system has been shown to satisfy graphically with this model corresponding to the pulsars 4U1820 - 30 (Mass= l.58M0 and radius= 9.1 km) [1] and Gen X - 3 (Mass= l.49M0 and radius= 10.136 km)[2]. The stability of the model is also discussed using some of the known stability criterion namely TOV equation, adiabatic index, Buchdahl condition and Herr era's cracking concept etc. The wid e applicability of our developed model has been justified with the numerical values of curre nt observational data set from various other known compact stars to a high degree of accuracy. Keywords: Einstein Field Equation; Anisotropic ; Stability; 41/1820 - 30; Gen X - 3. I. INTRODUCTION Compact star, being the last stage of stellar evo lution, has been the fi eld of active research work in the study of astrophysics since the discovery of particle neutron by Chadwick in the year 1932 [3 ]. At the end of stellar evo lution of a star during gravitationaJ collapse, the remnant which has high mass relative to their radius (10 - 12 k.m.) co mpared to ordinary atomic matter form the compact star. Depending on their masses it can be classified as white dwarfs, neutron stars, strange star or black hole. The densities involve in a typically white dwarf or neutron star is of the order of 10 14 - 10 15 gm/ cc. Discovery of neutron star [4] and observation of pulsars [5] have encouraged many researchers across the globe to model compact star theoretically. Compact objects are the natural laboratories provide a unique laboratory to study the structure of matter under extreme conditions like high gravity and density. Relativity (GR), which relates gravity with geometry becomes a key role to play to study compact star. The first solutions for Einstein field equations to describe the interior of the stellar structure were obtained by Karl Schwarzschild [6, 7] in 1916. One of the main task for a researcher is to develop a physically viable compact stellar analytical models within the framework of GR wh i ch are capable of desc ri bing recently observed pulsars. One can adopt two different approaches to develop relativistic stat ic se lf-gravitating compact stellar systems. First, by solving the Tolman-Oppenheimer-Volkov (TOY) equations (Phys. Rev. 55 374, (1939)) with the knowledge of the equ ation of state (EoS) corresponding to the material compositions of the star i.e., how the pressure depends on nuclear density. Due to lack of information regarding the particle interactions in extreme density, a lternative methods are often adopted where, amongst many techniques, such as prescribing the geometry or the fall-off behaviour of density /pressure/anisotropy/mass/some conditions are considered for the construction of the mode l. Also to overcome the difficulties involves with the non-linearity of Einstein field equations, various conditions like Karmarkar condition of embedding class one, conformal motion, conformally flat geometry etc. are adopted by several authors to ease the difficulty for solving the system of equations. • Electronic address: lipibaskey@gma il.com t Electronic address: dasshyam32l@gmail.com