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Anisotropic compact stellar model of embedding class-I satisfying Karmarkar’s condition in Vaidya and Tikekar spheroidal geometry

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Abstract

We present a class of solutions for a spherically symmetric anisotropic matter distribution in Vaidya and Tikekar spheroidal geometry. Making use of the Vaidya and Tikekar (VT) metric ansatz (J Astrophys Astron 3:325, 1982) for one of the metric functions \(g_{rr}\), we obtain the unknown metric function \(g_{tt}\) by utilizing the Karmakar’s embedding condition which makes the master equation tractable. The model parameters are fixed by utilizing the matching conditions of the interior spacetime and the exterior Schwarzschild solution at the boundary of the star where the radial pressure vanishes. The closed-form interior solution of the Einstein field equations thus obtained is shown to be capable of describing ultra-compact stellar objects where anisotropy might develop. The current estimated masses and radii of some other pulsars are utilized to show that the developed model meets all the requirements of a realistic star. The stability of the model is analyzed. The dependence of the curvature parameter K of the VT model, which characterizes a departure from homogeneous spherical distribution, is also investigated.

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Acknowledgements

RS and KC gratefully acknowledge support from the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India, under its Visiting Research Associateship Programme. SD is thankful to the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India, where a part of this work was carried out.

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Authors and Affiliations

  1. Department of Physics, P. D. Women’s College, Jalpaiguri, West Bengal, 735101, India

    Shyam Das

  2. Department of Physics, Cooch Behar Panchanan Barma University, Cooch Behar, West Bengal, 736101, India

    Ranjan Sharma

  3. Department of Physics, Government College of Education, Burdwan, West Bengal, 713102, India

    Koushik Chakraborty

  4. Department of Mathematics, Government General Degree College at Kushmandi, Dakshin Dinajpur, West Bengal, 733121, India

    Lipi Baskey

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  1. Shyam Das
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  2. Ranjan Sharma
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  3. Koushik Chakraborty
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  4. Lipi Baskey
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Correspondence to Ranjan Sharma.

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Das, S., Sharma, R., Chakraborty, K. et al. Anisotropic compact stellar model of embedding class-I satisfying Karmarkar’s condition in Vaidya and Tikekar spheroidal geometry. Gen Relativ Gravit 52, 101 (2020). https://doi.org/10.1007/s10714-020-02753-4

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