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Gravitational and Electromagnetic Field of an Isolated Positively Charged Particle

Received: 24 October 2020     Accepted: 20 November 2020     Published: 27 November 2020
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Abstract

A particle which is positively charged with spherically symmetry and non-rotating in empty space is taken to find out a metric or line element. The particle is under the influence of both gravitational and electro-magnetic field and the time component of this metric is depend on the combine effect of these two fields. Therefore in this work especial attention is given in Einstein gravitational and Maxwell’s electro-magnetic field equations. Einstein field equations are individually considered for gravitational and electro-magnetic fields in empty space for an isolated charged particle and combined them like two classical waves. To solve this new metric initially Schwarzschild like solution is used. There after a simple elegant and systematic method is used to determine the value of space coefficient and time coefficient of the metric. Finally to solve the metric the e-m field tensor is used from Maxwell’s electro-magnetic field equations. Thus in the metric the values of space and time coefficient is found a new one. The space and time coefficient in the new metric is not same in the metric as devised by Reissner and Nordstrom, The new space and time coefficient gives such an information about the massive body that at particular mass of a body can stop electro-magnetic interaction. Thus the new metric able to gives us some new information and conclusions.

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 6, Issue 4)
DOI 10.11648/j.ijamtp.20200604.11
Page(s) 54-60
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), 2020. Published by Science Publishing Group

Keywords

Metric, Gravitational Field, e-m Field, e-m Field Tensor

References
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[2] K. Schwarzschild, “On the gravitational field of a point-mass according to Einstein theory”, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl.; 189 (English translation) Abraham Zeimanov J, 1: 10-19 (1916).
[3] R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special Metrics”, Physical Review Letters, 11 (5): 237-240 (1963).
[4] J. B. Hartle, “Gravity-An introduction to Einstein’s general relativity”, Pearson, 5th ed., p 396- 404, (2012).
[5] T. Kaluza, “On the unification problem in physics”, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys): 966-972 (1921).
[6] O. Klein, “The atomicity of electricity as a quantum theory law”, Nature, 118: 516 (1926).
[7] O. Klein, “Quantum theory and five dimensional relativity”, Zeit. F. Physik 37: 895, Reproduced in O’Raiferaigh’s book (1926).
[8] A. S. Eddington, The mathematical theory of relativity”, Published by Cambridge University Press; 185-187 (1923).
[9] A. S. Eddington, “A generalisation of Weyl’s theory of the electromagnetic and gravitational field” Proc. Roy. Soc, A99, p104 (1921).
[10] G. Nordstrom, “On the energy of the gravitational field in Einstein theory”, Proc. Amsterdam Acad., 20, p1238 (1918).
[11] H. Reissner, “Uber die eigengravitation des elektrischen felds nach der Einsteinschen theorie”, Annalen der Physik (in German) 50 (9): 106-120 (1916).
[12] G. B. Jeffery, “The field of an electron on Einstein’s theory of gravitation”, Proceeding Royal Society, A99: 123-134 (1921).
[13] D. Finkelstein, “Past-future asymmetry of the gravitational field of a point particle”, Physical Review 110: 965-968 (1958).
[14] R. H. Boyer and R. W. Lindquist, “Maximal analytic extension of the Kerr metric”, J. Math. Phys. 8 (2): 265-281 (1967).
[15] E. Newman, A. Janis, “Note on the Kerr spinning-particle metric”, Journal of Mathematical Physics 6 (6); 915-917 (1965).
[16] E. Newman, E. Couch, K. Chinnapared, A. Exton, A. Prakash, R. Torrence, “Metric of a rotating Charged mass”, Journal of Mathematical Physics, 6 (6): 918-919 (1965).
[17] A. Einstein and W. de-Sitter, Proc. Nat. Acad. Sci., U. S. A., 18, p 213 (1932).
[18] A. Z. Friedman, Phys. A, 10 (1), p377 (1922).
[19] H. P. Robertson, Astro. Phys. J., 82, p284 (1935).
[20] S. Weinberg, “Gravitation and Cosmology”, Wiley India Private Ltd., p412-415 (2014).
[21] E. Witten, “Search for realistic Kaluza-Klein theory”, Nuclear Physics B 186 (3): 412-428 (1981).
[22] B. O’Neil, The geometry of Kerr Black holes”, Peters A K, Wellesley, Massachusetts, p-69 (1995).
[23] N. Bijan, “Schwarzschild-like solution for ellipsoidal celestial objects”, Int. J. Phys. Sci. 6 (6): 1426-1430 (2011).
[24] B. K. Borah, “Schwarzschild-like solution for the gravitational field of an isolated particle on the basis of 7-dimensional metric”, International Journal of Scientific and research publications, Vol. 3 (10): 1-8 (2013).
[25] R. J. Beach, “A classical Field Theory of Gravity and Electromagnetism”, Journal of Modern Physics, 5: 928-939 (2014).
[26] M. D. Yu-Ching, A derivation of the Kerr metric by ellipsoid coordinates transformation”, International Journal of Physical Science, 12 (11): 130-136 (2017).
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  • APA Style

    Bikash Kumar Borah. (2020). Gravitational and Electromagnetic Field of an Isolated Positively Charged Particle. International Journal of Applied Mathematics and Theoretical Physics, 6(4), 54-60. https://doi.org/10.11648/j.ijamtp.20200604.11

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    ACS Style

    Bikash Kumar Borah. Gravitational and Electromagnetic Field of an Isolated Positively Charged Particle. Int. J. Appl. Math. Theor. Phys. 2020, 6(4), 54-60. doi: 10.11648/j.ijamtp.20200604.11

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    AMA Style

    Bikash Kumar Borah. Gravitational and Electromagnetic Field of an Isolated Positively Charged Particle. Int J Appl Math Theor Phys. 2020;6(4):54-60. doi: 10.11648/j.ijamtp.20200604.11

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  • @article{10.11648/j.ijamtp.20200604.11,
      author = {Bikash Kumar Borah},
      title = {Gravitational and Electromagnetic Field of an Isolated Positively Charged Particle},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {6},
      number = {4},
      pages = {54-60},
      doi = {10.11648/j.ijamtp.20200604.11},
      url = {https://doi.org/10.11648/j.ijamtp.20200604.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20200604.11},
      abstract = {A particle which is positively charged with spherically symmetry and non-rotating in empty space is taken to find out a metric or line element. The particle is under the influence of both gravitational and electro-magnetic field and the time component of this metric is depend on the combine effect of these two fields. Therefore in this work especial attention is given in Einstein gravitational and Maxwell’s electro-magnetic field equations. Einstein field equations are individually considered for gravitational and electro-magnetic fields in empty space for an isolated charged particle and combined them like two classical waves. To solve this new metric initially Schwarzschild like solution is used. There after a simple elegant and systematic method is used to determine the value of space coefficient and time coefficient of the metric. Finally to solve the metric the e-m field tensor is used from Maxwell’s electro-magnetic field equations. Thus in the metric the values of space and time coefficient is found a new one. The space and time coefficient in the new metric is not same in the metric as devised by Reissner and Nordstrom, The new space and time coefficient gives such an information about the massive body that at particular mass of a body can stop electro-magnetic interaction. Thus the new metric able to gives us some new information and conclusions.},
     year = {2020}
    }
    

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    AU  - Bikash Kumar Borah
    Y1  - 2020/11/27
    PY  - 2020
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    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
    SP  - 54
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    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ijamtp.20200604.11
    AB  - A particle which is positively charged with spherically symmetry and non-rotating in empty space is taken to find out a metric or line element. The particle is under the influence of both gravitational and electro-magnetic field and the time component of this metric is depend on the combine effect of these two fields. Therefore in this work especial attention is given in Einstein gravitational and Maxwell’s electro-magnetic field equations. Einstein field equations are individually considered for gravitational and electro-magnetic fields in empty space for an isolated charged particle and combined them like two classical waves. To solve this new metric initially Schwarzschild like solution is used. There after a simple elegant and systematic method is used to determine the value of space coefficient and time coefficient of the metric. Finally to solve the metric the e-m field tensor is used from Maxwell’s electro-magnetic field equations. Thus in the metric the values of space and time coefficient is found a new one. The space and time coefficient in the new metric is not same in the metric as devised by Reissner and Nordstrom, The new space and time coefficient gives such an information about the massive body that at particular mass of a body can stop electro-magnetic interaction. Thus the new metric able to gives us some new information and conclusions.
    VL  - 6
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Author Information
  • Department of Physics, Jorhat Institute of Science and Technology, Jorhat, India

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