Anisotropic compact stars in the Buchdahl model: A comprehensive study

S. K. Maurya, Ayan Banerjee, M. K. Jasim, J. Kumar, A. K. Prasad, and Anirudh Pradhan
Phys. Rev. D 99, 044029 – Published 15 February 2019

Abstract

In this article we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized metric potential, namely, Buchdahl ansatz [Phys. Rev. D 116, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar and Finch-Skea. We developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that has a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter K and analyzed them in a uniform manner. As a result it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the frame work of anisotropic hypothesis, we consider analogue objects with similar mass and radii, such as LMC X-4, SMC X-1, EXO 1785-248 etc. to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of P=P(ρ), we demonstrate that equation of state (EoS) can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

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  • Received 24 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.044029

© 2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Gravitation, Cosmology & Astrophysics

Authors & Affiliations

S. K. Maurya*

  • Department of Mathematical and Physical Sciences, College of Arts and Science, University of Nizwa, Nizwa, Sultanate of Oman

Ayan Banerjee

  • Astrophysics and Cosmology Research Unit, University of KwaZulu Natal, Private Bag X54001, Durban 4000, South Africa

M. K. Jasim

  • Department of Mathematical and Physical Sciences, University of Nizwa, Nizwa 616, Sultanate of Oman

J. Kumar and A. K. Prasad§

  • Department of Applied Mathematics, Central University of Jharkhand, Ranchi 835205, India

Anirudh Pradhan

  • Department of Mathematics, Institute of Applied Sciences & Humanities, GLA University, Mathura 281 406, Uttar Pradesh, India

  • *sunil@unizwa.edu.om
  • ayan_7575@yahoo.co.in
  • mahmoodkhalid@unizwa.edu.om
  • §jitendark@gmail.com
  • pradhan.anirudh@gmail.com

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Issue

Vol. 99, Iss. 4 — 15 February 2019

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