Relativistic anisotropic models of ultra-dense stellar objects under embedding class I
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ORIGINAL PAPER
Relativistic anisotropic models of ultra-dense stellar objects under embedding class I S Gedela1,2, R K Bisht1 and N Pant1* 1
Department of Mathematics, National Defence Academy, Khadakwasla, Pune 411023, India 2
Department of Mathematics, SSJ Campus, Kumaun University, Almora 263601, India Received: 04 February 2020 / Accepted: 05 June 2020
Abstract: In this paper, we present a new class of exact solutions satisfying Einstein’s field and modified TOV-equations. The thermodynamic quantities of stellar matter like anisotropic pressures, baryon density, red-shift and velocity of sound have been investigated using the embedding class I methodology with the Karmarkar condition. The solutions satisfy the static stability criterion, energy conditions, stability factor, adiabatic index and causality condition. In addition to it, we perform complete graphical analysis of neutron stars in Vela X 1 and Her X 1 in the setting of the Karmarkar spacetime. Keywords: General relativity; Exact solution; Embedding class I; Anisotropy; Compact stars
1. Introduction Studies on relativistic stellar objects commenced in 1916, with a productive insight of the Schwarzschild vacuum solution of Einstein’s field equations (EFEs) with the forecasting of the existence of a black hole. In the same year, Schwarzschild [1] also gave a second solution of Einstein’s field equations which describes a uniform density compact star. Initially, compact stars were believed to be composed of isotropic perfect fluids only. Jeans [2] foretold that under extreme intricacy prevailing inside stellar objects, the difference of radial and tangential pressures, i.e., the measure of anisotropy is accented for a better realizing of the matter distribution. The anisotropy is considered as one of the key features of stellar configurations and plays a pivotal role in realistic modeling of relativistic stellar systems. The concept of anisotropy was proposed by Ruderman [3] and Canuto [4]. Bowers and Liang [5] were the first who reported the presence of anisotropic spheres in the framework of general relativity. Dev and Gleiser [6, 7] observed that the component of pressure anisotropy can cause drastic changes in many fundamental properties of highly compact
*Corresponding author, E-mail: [email protected] e-mail: [email protected]; e-mail: [email protected]
spheres. Recent observations on anisotropic pressures confirm the necessity of nonzero anisotropy in realistic modeling of highly compact spheres. The presences of 3A super-fluid [8], phase transitions [9], magnetic or strong electromagnetic field [10, 11], slow rotational motion [12], fluids of different types [13], pion condensation [14], etc., are some of the few reasons for the anisotropy in relativistic stellar systems. A systematic review regarding the origins and effects of local anisotropy in astrophysical objects can be found in [15, 16]. It is well known that EFEs describe gravity as geometry of space-time due to the presence of the matter distribution. Based on embed
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