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Some anisotropic planar stellar models

Z. Yousaf

Department of Mathematics, University of the Punjab, Quaid-i-Azam Campus, Lahore 54590, Pakistan

E-mail Address: zeeshan.math@pu.edu.pk

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and

M. Zaeem-ul-Haq Bhatti

Department of Mathematics, University of the Punjab, Quaid-i-Azam Campus, Lahore 54590, Pakistan

E-mail Address: mzaeem.math@pu.edu.pk

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https://doi.org/10.1142/S0219887818501608Cited by:13 (Source: Crossref)

Abstract

The aim of this paper is to investigate the influence of expansion-free condition and cosmological constant in the modeling of planar relativistic self-gravitating objects. For this purpose, we have considered a non-static diagonally oriented planar geometry that is coupled with locally anisotropic non-radiating matter configurations. Firstly, we have explored the factor responsible for maintaining conformal flat state by relating tidal forces with matter dynamical variables. Then, we have smoothly joined our relativistic interior with the exterior one through Darmois junction conditions in the $Λ$ -dominated epoch. We have also shown that the well-known perfect fluid Skripkin model has disobeyed matching conditions for the case of planar system with cosmological constant. Lastly, we have inspected family of exact analytical solutions of Einstein- $Λ$ field equations with various backgrounds, like, an/isotropic matter, separable energy density and barotropic equation of state.

Keywords:

PACS: 04.20.Ha, 04.20.Jb, 04.40.Dg, 04.40.Nr

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