American Journal of Physics and Applications

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Generating Theorems for Charged Anisotropy in General Relativity

Received: 24 March 2016    Accepted:     Published: 25 March 2016
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Abstract

For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.

DOI 10.11648/j.ajpa.20160402.13
Published in American Journal of Physics and Applications (Volume 4, Issue 2, March 2016)
Page(s) 50-56
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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

General Relativity, Charged Anisotropy, Fluid Spheres

References
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[2] P. Boonserm, M. Visser and S. Weinfurtner, “Generating perfect fluid spheres in general relativity”, Phys. Rev. D 71 (2005) 124037 [arXiv: gr-qc/0503007].
[3] S. Carroll, “Spacetime and geometry: an introduction to general relativity”, Pearson new international edition, U.S.A., Pearson Education Limited, 2014.
[4] H. Bondi, “Spherically symmetrical models in general relativity”, Mon. Not. Roy. Astron. Soc. 107 (1947) 410.
[5] H. A. Buchdahl, “General relativistic fluid spheres”, Phys. Rev. 116 (1959) 1027-1034.
[6] M. S. R. Delgaty and K. Lake, “Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein’s equations”, Compute. Phys. Commun. 115 (1998) 395 [arXiv: gr-qc/9809013].
[7] P. Boonserm, M. Visser and S. Weinfurtner, “Solution generating theorems for the TOV equation”, Phys. Rev. D 76 (2007) 044024 [arXiv: gr-qc/0607001].
[8] A. Sulaksono, “Anisotropic pressure and hyperon in neutron stars,” Int. J. Mod. Phys. E 24 (2015) 01, 1550007 [arXiv: 1412.7274 [nucl-tn]].
[9] P. Boonserm, T. Ngampitipan and M. Visser, “Mimicking static anisotropic fluid spheres in general relativity”, International Journal of Modern Physics D (2015): 1650019 [arXiv: 1501.07044v3 [gr-qc]].
[10] P. Boonserm, “Some exact solution in general relativity”, MSc. Thesis, Victoria University of Wellington, 2006.
[11] Chandrasekhar, S. (1998). The Mathematical Theory of Black Holes (Reprinted ed.). Oxford University Press. p. 205. ISBN 0-19850370-9. Retrieved 13 May 2013.
[12] K. Komathiraj ans S. D. Maharaj, “A class of charged relativistic spheres”, Mathematical and Computational Applications 15, 665-673, 2010.
[13] Patel, L. K., and N. P. Mehta. "An exact model of an anisotropic relativistic sphere." Australian Journal of Physics 48.4 (1995): 635-644.
[14] Ray, Saibal, and Basanti Das, “Tolman-Bayin type static charged fluid spheres in general relativity.” Monthly Notices of the Royal Astronomical Society 349.4 (2004), 1331-1334.
[15] K. Thairatana, “Transformation for perfect fluid spheres in isotropic coordinates”, MSc. Thesis, Chulalongkorn University, 2013.
[16] K. Lake, “all static spherically symmetric perfect fluid solutions of Einstein’s equation”, Phys. Rev. D 67 (2003) 104015 [gr-qc/0209104].
[17] S. Rahman and M. Visser, “Space-time geometry of static fluid spheres”, Class. Quant. Grav. 19 (2002) 935 [gr-qc/0103065].
[18] S. S. Bayin, “Anisotropic fluid spheres in general relativity”, Phys. Rev. D 26 (1982) 1262.
[19] L. Herrera, J. Ospino and A. Di Prisco, “All static spherically symmetric anisotropic solutions of Einstein’s equation”, Phys. Rev. D 77 (2008) 027502 [arXiv: 0712.0713 [gr-qc]].
Author Information
  • Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand

  • Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand

  • Faculty of Science, Chandrakasem Rajabhat University, Bangkok, Thailand

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    Napasorn Jongjittanon, Petarpa Boonserm, Tritos Ngampitipan. (2016). Generating Theorems for Charged Anisotropy in General Relativity. American Journal of Physics and Applications, 4(2), 50-56. https://doi.org/10.11648/j.ajpa.20160402.13

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    ACS Style

    Napasorn Jongjittanon; Petarpa Boonserm; Tritos Ngampitipan. Generating Theorems for Charged Anisotropy in General Relativity. Am. J. Phys. Appl. 2016, 4(2), 50-56. doi: 10.11648/j.ajpa.20160402.13

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    AMA Style

    Napasorn Jongjittanon, Petarpa Boonserm, Tritos Ngampitipan. Generating Theorems for Charged Anisotropy in General Relativity. Am J Phys Appl. 2016;4(2):50-56. doi: 10.11648/j.ajpa.20160402.13

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  • @article{10.11648/j.ajpa.20160402.13,
      author = {Napasorn Jongjittanon and Petarpa Boonserm and Tritos Ngampitipan},
      title = {Generating Theorems for Charged Anisotropy in General Relativity},
      journal = {American Journal of Physics and Applications},
      volume = {4},
      number = {2},
      pages = {50-56},
      doi = {10.11648/j.ajpa.20160402.13},
      url = {https://doi.org/10.11648/j.ajpa.20160402.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajpa.20160402.13},
      abstract = {For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.},
     year = {2016}
    }
    

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    T1  - Generating Theorems for Charged Anisotropy in General Relativity
    AU  - Napasorn Jongjittanon
    AU  - Petarpa Boonserm
    AU  - Tritos Ngampitipan
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    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
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    EP  - 56
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajpa.20160402.13
    AB  - For describing the interior of a spherical object in the general relativistic frame, some objects can be considered using the concept of perfect fluid spheres for simplicity. The absence of heat conduction and shear stress, and the presence of isotropic pressure are the characteristics of perfect fluid spheres. Previous works in this field constitute finding solutions for perfect fluid spheres in various coordinates. In this work, we are interested in generating anisotropic solution for fluid spheres. The particular property of anisotropy, which differs from the property of perfect fluid spheres, is that the radial pressure and the transverse pressure are not equal. One cause of anisotropy is the presence of charge inside an object. Anisotropic fluid spheres are models for describing a charged star such as a neutron star. An important tool in studying fluid sphere solutions is the solution generating algorithm. This technique can be used to generate new solution from known solutions without having to solve Einstein’s equation directly. The solution generating theorems for anisotropic fluid spheres are constructed in terms of the metric of spacetime. The other purpose is to classify the types of solution into seed and non-seed metrices.
    VL  - 4
    IS  - 2
    ER  - 

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