American Journal of Modern Physics

| Peer-Reviewed |

New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model

Received: 27 January 2017    Accepted: 13 February 2017    Published: 07 March 2017
Views:       Downloads:

Share This Article

Abstract

Exact solution for spherically symmetric isotropic charged fluid sphere are investigated relativistic model of an electrically charged compact star, and energy density associated with the electric fluids is on the same order of magnitude as the energy density of fluid matter itself. The analytic solution depicts a unique static charged configuration of quark matter with radius R~9 km and total mass M~2.5M. And try to inspect the velocity of sound approximately 1/√3 which is similar to the attitude of SQM (Strange Quark matter). Adiabatic index conform the stability of star if the adiabatic index is less than 4/3. Based on an analytic model in the recent work, the applicable values of physical quantities have been calculated by accepting the estimated masses and radii of some well-known strange star candidates like PSR J1903+327, Her X-1, Cen X-3, EXO 1785-248.

DOI 10.11648/j.ajmp.20170601.13
Published in American Journal of Modern Physics (Volume 6, Issue 1, January 2017)
Page(s) 16-22
Creative Commons

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

Exact Solution, Einstein – Maxwell, Reissner – Nordström, Relativistic Astrophysics, Compact Star, Equation of State

References
[1] Pant, N., Rajasekhara, S.: Variety of well-behaved parametric classes of relativistic charged fluid spheres in general relativity. Astrophys. Space Sci. 333, 161-168 (2011). doi: 10.1007/s10509-011-0607-z.
[2] Nduka, A.: Charged fluid sphere in general relativity, Gen. Relativ. Gravit. 7 (1976) 493―499, doi: 10.1007/BF00766408.
[3] Nduka, A.: Static solutions of Einstein’s field equations for charged spheres of fluid, Acta Phys. Pol. B 9 (1978) 596―571.
[4] Mehra, A. L., Bohra, B. L.: Gen. Relativ. Gravit. 11, 333–336 (1979). doi: 10.1007/BF00759275.
[5] Pant, N., Faruqi, S.: Relativistic modelling of a superdense star containing a charged perfect fluid, Gravit. Cosmol. 18 (2012) 204―210, doi: 10.1134/S0202289312030073.
[6] Pant, N., Mehta, R. N., Tewari, B. C., Astrophys. Space Sci. 327, 279 (2010).
[7] Pant, N., Tewari, B. C., Astroph. Space Sci. 331, 645 (2010).
[8] Pinheiro, G. and Chan, R., Gen. Rel. Grav. 40, 2149 (2008).
[9] Usov, V. V.: Phys. Rev. D, Part. Fields 70, 067301 (2004). doi: 10.1103/PhysRevD.70.067301.
[10] Usov, V. V., et al.: Astrophys. J. 620, 915 (2005). doi: 10.1086/427074.
[11] Negreiros, R. P., et al.: Phys. Rev. D 82, 103010 (2010). doi: 10.1103/PhysRevD.82.103010.
[12] Farhi, E., Olinto, A., 1986, Astrophys. J. 310, 261.
[13] Negreiros, R. P., et al. Phys. Rev. D 80, 083006 (2009). doi: 10.1103/PhysRevD.80.083006.
[14] Jaikumar, P., Reddy, S., Steiner, A. W.: Phys. Rev. Lett. 96 (2006) 041101.
[15] Tolman, R. C.: Static solutions of Einstein’s field equations for spheres of fluid. Phys. Rev. 55, 364–373 (1939). doi: 10.1103/PhysRev.55.364.
[16] Dionysiou, D. D.: Astrophys. Space Sci. 85, 331 (1982). doi: 10.1007/BF00653455.
[17] Durgapal, M. C.: A class of new exact solutions in general relativity. J. Phys. A, Math. Gen. 15, 2637–2644 (1982). doi: 10.1088/0305-4470/15/8/039.
[18] Lake, K.: All static spherically symmetric perfect-fluid solutions of Einstein’s equations. Phys. Rev. D 67, 104015 (2003). doi: 10.1103/PhysRevD.67.104015.
[19] Maurya, S. K., Gupta, Y. K.: Astrophys. Space Sci. 334, 145 (2011a). doi: 10.1007/s10509-011-0705-y.
[20] Maurya, S. K., Gupta, Y. K.: Astrophys. Space Sci. 334, 301 (2011b). doi: 10.1007/s10509-011-0736-4.
[21] Lattimer, J. M., Prakash, M.: Phys. Rev. Lett. 94, 111101 (2005). doi: 10.1103/PhysRevLett.94.111101.
[22] H. Heintzmann, Z. Physik 228, 489 (1969). doi: 10.1007/BF1558346.
[23] Murad, M. H., Fatema, S.: Int. J. Theor. Phys. 52, 4342 (2013a). doi: 10.1007/s10773-013-1752-7.
[24] Abreu, H. Hernández, L. A Nún᷉ez, Class. Q. Grav. 24, 4631 (2007). doi: 10.1088/0264-9381/24/18/005.
[25] Li, X.-D., et al.: Phys. Rev. Lett. 83, 3776 (1999). doi: 10.1103/PhysRevLett.83.3776.
[26] Dey, M., et al.: Phys. Lett. B 438, 123 (1998). doi: 10.1016/S0370-2693 (98)00935-6.
[27] Weber, F.: Prog. Part. Nucl. Phys. 54, 193 (2005). doi: 10.1016/j.ppnp.2004.07.001.
[28] Gangopadhyay, T., et al.: (2013). doi: 10.1093/mnras/stt401.
Author Information
  • Department of Mathematics and Natural Sciences, BRAC University, Dhaka, Bangladesh

  • Science and Math Program, Asian University for Women, Chittagong, Bangladesh

Cite This Article
  • APA Style

    A. H. M. Mahbubur Rahman, Md. Rubayet Rahman. (2017). New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model. American Journal of Modern Physics, 6(1), 16-22. https://doi.org/10.11648/j.ajmp.20170601.13

    Copy | Download

    ACS Style

    A. H. M. Mahbubur Rahman; Md. Rubayet Rahman. New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model. Am. J. Mod. Phys. 2017, 6(1), 16-22. doi: 10.11648/j.ajmp.20170601.13

    Copy | Download

    AMA Style

    A. H. M. Mahbubur Rahman, Md. Rubayet Rahman. New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model. Am J Mod Phys. 2017;6(1):16-22. doi: 10.11648/j.ajmp.20170601.13

    Copy | Download

  • @article{10.11648/j.ajmp.20170601.13,
      author = {A. H. M. Mahbubur Rahman and Md. Rubayet Rahman},
      title = {New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model},
      journal = {American Journal of Modern Physics},
      volume = {6},
      number = {1},
      pages = {16-22},
      doi = {10.11648/j.ajmp.20170601.13},
      url = {https://doi.org/10.11648/j.ajmp.20170601.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmp.20170601.13},
      abstract = {Exact solution for spherically symmetric isotropic charged fluid sphere are investigated relativistic model of an electrically charged compact star, and energy density associated with the electric fluids is on the same order of magnitude as the energy density of fluid matter itself. The analytic solution depicts a unique static charged configuration of quark matter with radius R~9 km and total mass M~2.5M⊙. And try to inspect the velocity of sound approximately 1/√3 which is similar to the attitude of SQM (Strange Quark matter). Adiabatic index conform the stability of star if the adiabatic index is less than 4/3. Based on an analytic model in the recent work, the applicable values of physical quantities have been calculated by accepting the estimated masses and radii of some well-known strange star candidates like PSR J1903+327, Her X-1, Cen X-3, EXO 1785-248.},
     year = {2017}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - New Class of Heintzmann Exact Solution in General Relativity for an Isotropic Charged Stellar Model
    AU  - A. H. M. Mahbubur Rahman
    AU  - Md. Rubayet Rahman
    Y1  - 2017/03/07
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajmp.20170601.13
    DO  - 10.11648/j.ajmp.20170601.13
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 16
    EP  - 22
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20170601.13
    AB  - Exact solution for spherically symmetric isotropic charged fluid sphere are investigated relativistic model of an electrically charged compact star, and energy density associated with the electric fluids is on the same order of magnitude as the energy density of fluid matter itself. The analytic solution depicts a unique static charged configuration of quark matter with radius R~9 km and total mass M~2.5M⊙. And try to inspect the velocity of sound approximately 1/√3 which is similar to the attitude of SQM (Strange Quark matter). Adiabatic index conform the stability of star if the adiabatic index is less than 4/3. Based on an analytic model in the recent work, the applicable values of physical quantities have been calculated by accepting the estimated masses and radii of some well-known strange star candidates like PSR J1903+327, Her X-1, Cen X-3, EXO 1785-248.
    VL  - 6
    IS  - 1
    ER  - 

    Copy | Download

  • Sections