International Journal of Astrophysics and Space Science

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Analytical Models for Quark Stars with Van Der Waals Modified Equation of State

Received: Sep. 07, 2019    Accepted: Oct. 15, 2019    Published: Oct. 24, 2019
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Abstract

Stellar models consisting of spherically symmetric distribution of charged matter locally anisotropic in strong gravitational fields have been widely considered in the frame of general relativity. These investigations require the generation of exact models through the resolution of the Einstein-Maxwell system of equations. The presence of charge produces values for redshifts, luminosity and mass for the stars different in relation to neutral matter. Some applications for dense charged matter we have them in the description of quark stars, spheres with linear or non-linear equation of state, hybrid stars and accreting process in compact objects where the matter acquires large amounts of electric charge. In this paper, we studied the behavior of relativistic compact objects with anisotropic matter distribution considering Van der Waals modified equation of state proposed in 2013 for Malaver and a gravitational potential Z(x) that depends on an adjustable parameter α in order to integrate analytically the field equations. They generalize the ideal gas law based on plausible reasons that real gases do not act ideally. New exact solutions of the Einstein-Maxwell system are generated and the physical variables as the energy density, radial pressure, mass function, anisotropy factor and the metric functions are written in terms of elementary and polynomial functions. We obtained expressions for radial pressure, density and mass of the stellar object physically acceptable with two different values of the adjustable parameter. The proposed models satisfy all physical features of a realistic star.

DOI 10.11648/j.ijass.20190705.11
Published in International Journal of Astrophysics and Space Science ( Volume 7, Issue 5, October 2019 )

This article belongs to the Special Issue Modelling and Simulation of Magnetars and Stellar Objects

Page(s) 49-58
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Relativistic Compact Objects, Gravitational Potential, Einstein-Maxwell System, Radial Pressure, Anisotropy Factor, Matter Distribution, General Relativity, Einstein Field Equations

References
[1] Kuhfitting, P. K. (2011). Some remarks on exact wormhole solutions, Adv. Stud. Theor. Phys., 5, 365-367.
[2] Bicak, J. (2006). Einstein equations: exact solutions, Encyclopaedia of Mathematical Physics, 2, 165-173.
[3] Malaver, M. (2013). Black Holes, Wormholes and Dark Energy Stars in General Relativity. Lambert Academic Publishing, Berlin. ISBN: 978-3-659-34784-9.
[4] Komathiraj, K., and Maharaj, S. D. (2008). Classes of exact Einstein-Maxwell solutions, Gen. Rel. Grav., 39, 2079-2093.
[5] Sharma, R., Mukherjee, S and Maharaj, S. D. (2001). General solution for a class of static charged stars, Gen. Rel. Grav., 33, 999-110.
[6] Thirukkanesh, S. and Ragel, F. C. (2012). Exact anisotropic sphere with polytropic equation of state, PRAMANA-Journal of physics, 78 (5), 687-696.
[7] Itoh, N. (1970). Hydrostatic equilibrium of hypothetical quark stars, Prog. Theor. Phys.44, 291-292.
[8] Komathiraj, K., and Maharaj, S. D. (2007). Analytical models for quark stars. Int. J. Mod. Phys. D16, 1803-1811.
[9] Schwarzschild, K. (1916). Uber das Gravitationsfeld einer Kugel aus inkompressibler Flussigkeit nach der Einsteinschen Theorie. Math. Phys. Tech, 424-434.
[10] Tolman, R. C. (1939). Static Solutions of Einstein's Field Equations for Spheres of Fluid. Phys. Rev., 55 (4), 364-373.
[11] Oppenheimer, J. R. and Volkoff, G. (1939). On Massive Neutron Cores. Phys. Rev., 55 (4), 374-381.
[12] Chandrasekahr, S. (1931). The Maximum Mass of Ideal White Dwarfs. Astrophys. J, 74, 81-82.
[13] Baade, W. and Zwicky, F. (1934). On Super-novae. Proc. Nat. Acad. Sci. U.S 20 (5), 254-259.
[14] Cosenza, M., Herrera, L., Esculpi, M. and Witten, L. (1981). Some Models of Anisotropic Spheres in General Relativity, J. Math. Phys, 22 (1), 118.
[15] Gokhroo, M. K. and Mehra, A. L. (1994). Anisotropic Spheres with Variable Energy Density in General Relativity. Gen. Relat. Grav, 26 (1), 75-84.
[16] Esculpi, M., Malaver, M. and Aloma, E. (2007). A Comparative Analysis of the Adiabatic Stability of Anisotropic Spherically Symmetric solutions in General Relativity. Gen. Relat. Grav, 39 (5), 633-652.
[17] Malaver, M. (2018). Generalized Nonsingular Model for Compact Stars Electrically Charged. World Scientific News, 92 (2), 327-339.
[18] Malaver, M. (2018). Some new models of anisotropic compact stars with quadratic equation of state. World Scientific News, 109, 180-194.
[19] Chan R., Herrera L. and Santos N. O. (1992). Dynamical instability in the collapse of anisotropic matter. Class. Quantum Grav, 9 (10), L133.
[20] Malaver, M. (2017). New Mathematical Models of Compact Stars with Charge Distributions. International Journal of Systems Science and Applied Mathematics, 2 (5), 93-98.
[21] Cosenza M., Herrera L., Esculpi M. and Witten L. (1982). Evolution of radiating anisotropic spheres in general relativity. Phys. Rev. D, 25 (10), 2527-2535.
[22] Herrera L. (1992). Cracking of self-gravitating compact objects. Phys. Lett. A, 165, 206-210.
[23] Herrera L. and Ponce de Leon J. (1985). Perfect fluid spheres admitting a one‐parameter group of conformal motions. J. Math. Phys, 26, 778.
[24] Herrera L. and Nunez L. (1989). Modeling 'hydrodynamic phase transitions' in a radiating spherically symmetric distribution of matter. The Astrophysical Journal, 339 (1), 339-353.
[25] Herrera L., Ruggeri G. J. and Witten L. (1979). Adiabatic Contraction of Anisotropic Spheres in General Relativity. The Astrophysical Journal, 234, 1094-1099.
[26] Herrera L., Jimenez L., Leal L., Ponce de Leon J., Esculpi M and Galina V. (1984). Anisotropic fluids and conformal motions in general relativity. J. Math. Phys, 25, 3274.
[27] Bowers, R. L. and Liang, E. P. T. (1974). Anisotropic Spheres in General Relativity, The Astrophysical Journal, 188, 657-665.
[28] Sokolov. A. I. (1980). Phase transitions in a superfluid neutron liquid. Sov. Phys. JETP, 52 (4), 575-576.
[29] Usov, V. V. (2004). Electric fields at the quark surface of strange stars in the color- flavor locked phase. Phys. Rev. D, 70 (6), 067301.
[30] Komathiraj, K. and Maharaj, S. D. (2008). Classes of exact Einstein-Maxwell solutions, Gen. Rel. Grav. 39 (12), 2079-2093.
[31] Thirukkanesh, S. and Maharaj, S. D. (2008). Charged anisotropic matter with a linear equation of state. Class. Quantum Gravity, 25 (23), 235001.
[32] Maharaj, S. D., Sunzu, J. M. and Ray, S. (2014). Some simple models for quark stars. Eur. Phys. J. Plus, 129, 3.
[33] Thirukkanesh, S. and Ragel, F. C. (2013). A class of exact strange quark star model. PRAMANA-Journal of physics, 81 (2), 275-286.
[34] Thirukkanesh, S. and Ragel, F.C. (2014). Strange star model with Tolmann IV type potential, Astrophysics and Space Science, 352(2), 743-749.
[35] Feroze, T. and Siddiqui, A. (2011). Charged anisotropic matter with quadratic equation of state. Gen. Rel. Grav, 43, 1025-1035.
[36] Feroze, T. and Siddiqui, A. (2014). Some Exact Solutions of the Einstein-Maxwell Equations with a Quadratic Equation of State. Journal of the Korean Physical Society, 65 (6), 944-947.
[37] Sunzu, J. M, Maharaj, S. D., Ray, S. (2014). Quark star model with charged anisotropic matter. Astrophysics. Space. Sci, 354, 517-524.
[38] Pant, N., Pradhan, N., Malaver, M. (2015). Anisotropic fluid star model in isotropic coordinates. International Journal of Astrophysics and Space Science. Special Issue: Compact Objects in General Relativity. 3 (1), 1-5.
[39] Malaver, M. (2014). Strange Quark Star Model with Quadratic Equation of State. Frontiers of Mathematics and Its Applications, 1 (1), 9-15.
[40] Malaver, M. (2018). Charged anisotropic models in a modified Tolman IV spacetime. World Scientific News, 101, 31-43.
[41] Malaver, M. (2018). Charged stellar model with a prescribed form of metric function y (x) in a Tolman VII spacetime. World Scientific News, 108, 41-52.
[42] Malaver, M. (2016). Classes of relativistic stars with quadratic equation of state. World Scientific News, 57, 70-80.
[43] Malaver, M. (2009). Análisis comparativo de algunos modelos analíticos para estrellas de quarks, Revista Integración, 27 (2), 125-133.
[44] Bombaci, I. (1997). Observational evidence for strange matter in compact objects from the x- ray burster 4U 1820-30, Phys. Rev, C55, 1587- 1590.
[45] Dey, M., Bombaci, I, Dey, J, Ray, S and. Samanta, B. C. (1998). Strange stars with realistic quark vector interaction and phenomenological density-dependent scalar potential, Phys. Lett, B438, 123-128.
[46] Takisa, P. M., Maharaj, S. D. (2013). Some charged polytropic models. Gen. Rel. Grav, 45, 1951-1969.
[47] Malaver, M. (2013). Analytical model for charged polytropic stars with Van der Waals Modified Equation of State, American Journal of Astronomy and Astrophysics, 1 (4), 37-42.
[48] Mak, M. K., and Harko, T. (2004). Quark stars admitting a one-parameter group of conformal motions, Int. J. Mod. Phys D, 13 (1), 149-156.
[49] Malaver, M. (2013). Regular model for a quark star with Van der Waals modified equation of state, World Applied Programming., 3, 309-313.
[50] Durgapal, M. C., Bannerji, R. (1983). New analytical stellar model in general relativity. Phys. Rev. D27, 328-331.
[51] Delgaty, M. S. R and Lake, K. (1998). Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations, Comput. Phys. Commun. 115, 395-415.
[52] Kalam, M., Usmani, A. A., Rahaman, F., Hossein, M. Sk., Karar, I. and Sharma, R. (2013). A relativistic model for Strange Quark Star, Int. J. Theor. Phys., 52 (9), 3319-3328.
[53] Hossein, M. Sk., Rahaman, F., Naskar, J and Kalam, M. (2012). Anisotropic Compact stars with variable cosmological constant, Int. J. Mod. Phys D, 21 (13), 1250088.
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  • APA Style

    Manuel Malaver, Hamed Daei Kasmaei. (2019). Analytical Models for Quark Stars with Van Der Waals Modified Equation of State. International Journal of Astrophysics and Space Science, 7(5), 49-58. https://doi.org/10.11648/j.ijass.20190705.11

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    ACS Style

    Manuel Malaver; Hamed Daei Kasmaei. Analytical Models for Quark Stars with Van Der Waals Modified Equation of State. Int. J. Astrophys. Space Sci. 2019, 7(5), 49-58. doi: 10.11648/j.ijass.20190705.11

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    AMA Style

    Manuel Malaver, Hamed Daei Kasmaei. Analytical Models for Quark Stars with Van Der Waals Modified Equation of State. Int J Astrophys Space Sci. 2019;7(5):49-58. doi: 10.11648/j.ijass.20190705.11

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  • @article{10.11648/j.ijass.20190705.11,
      author = {Manuel Malaver and Hamed Daei Kasmaei},
      title = {Analytical Models for Quark Stars with Van Der Waals Modified Equation of State},
      journal = {International Journal of Astrophysics and Space Science},
      volume = {7},
      number = {5},
      pages = {49-58},
      doi = {10.11648/j.ijass.20190705.11},
      url = {https://doi.org/10.11648/j.ijass.20190705.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijass.20190705.11},
      abstract = {Stellar models consisting of spherically symmetric distribution of charged matter locally anisotropic in strong gravitational fields have been widely considered in the frame of general relativity. These investigations require the generation of exact models through the resolution of the Einstein-Maxwell system of equations. The presence of charge produces values for redshifts, luminosity and mass for the stars different in relation to neutral matter. Some applications for dense charged matter we have them in the description of quark stars, spheres with linear or non-linear equation of state, hybrid stars and accreting process in compact objects where the matter acquires large amounts of electric charge. In this paper, we studied the behavior of relativistic compact objects with anisotropic matter distribution considering Van der Waals modified equation of state proposed in 2013 for Malaver and a gravitational potential Z(x) that depends on an adjustable parameter α in order to integrate analytically the field equations. They generalize the ideal gas law based on plausible reasons that real gases do not act ideally. New exact solutions of the Einstein-Maxwell system are generated and the physical variables as the energy density, radial pressure, mass function, anisotropy factor and the metric functions are written in terms of elementary and polynomial functions. We obtained expressions for radial pressure, density and mass of the stellar object physically acceptable with two different values of the adjustable parameter. The proposed models satisfy all physical features of a realistic star.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Analytical Models for Quark Stars with Van Der Waals Modified Equation of State
    AU  - Manuel Malaver
    AU  - Hamed Daei Kasmaei
    Y1  - 2019/10/24
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    DO  - 10.11648/j.ijass.20190705.11
    T2  - International Journal of Astrophysics and Space Science
    JF  - International Journal of Astrophysics and Space Science
    JO  - International Journal of Astrophysics and Space Science
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    EP  - 58
    PB  - Science Publishing Group
    SN  - 2376-7022
    UR  - https://doi.org/10.11648/j.ijass.20190705.11
    AB  - Stellar models consisting of spherically symmetric distribution of charged matter locally anisotropic in strong gravitational fields have been widely considered in the frame of general relativity. These investigations require the generation of exact models through the resolution of the Einstein-Maxwell system of equations. The presence of charge produces values for redshifts, luminosity and mass for the stars different in relation to neutral matter. Some applications for dense charged matter we have them in the description of quark stars, spheres with linear or non-linear equation of state, hybrid stars and accreting process in compact objects where the matter acquires large amounts of electric charge. In this paper, we studied the behavior of relativistic compact objects with anisotropic matter distribution considering Van der Waals modified equation of state proposed in 2013 for Malaver and a gravitational potential Z(x) that depends on an adjustable parameter α in order to integrate analytically the field equations. They generalize the ideal gas law based on plausible reasons that real gases do not act ideally. New exact solutions of the Einstein-Maxwell system are generated and the physical variables as the energy density, radial pressure, mass function, anisotropy factor and the metric functions are written in terms of elementary and polynomial functions. We obtained expressions for radial pressure, density and mass of the stellar object physically acceptable with two different values of the adjustable parameter. The proposed models satisfy all physical features of a realistic star.
    VL  - 7
    IS  - 5
    ER  - 

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Author Information
  • Bijective Physics Group, Bijective Physics Institute, Idrija, Slovenia; Department of Basic Sciences, Maritime University of the Caribbean, Catia la Mar, Venezuela

  • Department of Applied Mathematics, Islamic Azad University-Central Tehran Branch, Tehran, Iran

  • Section