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Gravitational Collapse and Singularities in Some Non-Schwarzschild's Space-Times

Received: 6 November 2018     Accepted: 19 November 2018     Published: 7 January 2019
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Abstract

Singularities in three non-Schwarzschild space-times: Minkowski, Friedman-Lemaitre-Robertson-Walker and Reissner-Nordstromare investigated. Gravitational collapse in the Schwarzschild solution is obvious and widely studied. However, gravitational collapse should not be limited to Schwarzschild solution only as interesting findings exist in other metric fields. The Ricci curvature scalar for each space-time is evaluated and used in the determination of true curvature singularities. The Ricci scalar has proved to be very effective in determining the presence of singularities or otherwise in space-time geometry. Results indicate that there are inherent singularities in components of space-time in all three cases. Gravitational singularities in Minkowski space are found to be consequences of the choice of coordinate. Minkowksi space possesses only coordinate singularities and no curvature singularity. This differs with Schwarzschild’s metric which has true curvature singularity. Friedman-Lemaitre-Robertson-Walker (FLRW) and Reissner-Nordstrom metrics have true curvature singularities. Gravitational collapse in the FLRW metric yields a curvature singularity which shows the universe started a finite time ago. Cosmic strings, white holes and blackholes are deduced from the Reissner-Nordstrom singularities. Reissner-Nordstrom solution show that the addition of small amounts of electric charge or angular momentum could completely alter the nature of the singularity, causing the matter to fall through a ‘wormhole’ and emerge into another universe. Analysis of gravitational collapse in this article provides one of the most exciting research frontiers in gravitation physics and high energy astrophysics; as the debate on their physical existence persists.

Published in International Journal of Astrophysics and Space Science (Volume 6, Issue 6)
DOI 10.11648/j.ijass.20180606.11
Page(s) 93-100
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), 2019. Published by Science Publishing Group

Keywords

Singularities, Non-Schwarzschild, Reissner-Nordstrom, Curvature, Minkowski, Space-Time

References
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  • APA Style

    Chifu Ebenezer Ndikilar, Abu Ovansa Samson, Hafeez Yusuf Hafeez. (2019). Gravitational Collapse and Singularities in Some Non-Schwarzschild's Space-Times. International Journal of Astrophysics and Space Science, 6(6), 93-100. https://doi.org/10.11648/j.ijass.20180606.11

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    ACS Style

    Chifu Ebenezer Ndikilar; Abu Ovansa Samson; Hafeez Yusuf Hafeez. Gravitational Collapse and Singularities in Some Non-Schwarzschild's Space-Times. Int. J. Astrophys. Space Sci. 2019, 6(6), 93-100. doi: 10.11648/j.ijass.20180606.11

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    AMA Style

    Chifu Ebenezer Ndikilar, Abu Ovansa Samson, Hafeez Yusuf Hafeez. Gravitational Collapse and Singularities in Some Non-Schwarzschild's Space-Times. Int J Astrophys Space Sci. 2019;6(6):93-100. doi: 10.11648/j.ijass.20180606.11

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  • @article{10.11648/j.ijass.20180606.11,
      author = {Chifu Ebenezer Ndikilar and Abu Ovansa Samson and Hafeez Yusuf Hafeez},
      title = {Gravitational Collapse and Singularities in Some Non-Schwarzschild's Space-Times},
      journal = {International Journal of Astrophysics and Space Science},
      volume = {6},
      number = {6},
      pages = {93-100},
      doi = {10.11648/j.ijass.20180606.11},
      url = {https://doi.org/10.11648/j.ijass.20180606.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20180606.11},
      abstract = {Singularities in three non-Schwarzschild space-times: Minkowski, Friedman-Lemaitre-Robertson-Walker and Reissner-Nordstromare investigated. Gravitational collapse in the Schwarzschild solution is obvious and widely studied. However, gravitational collapse should not be limited to Schwarzschild solution only as interesting findings exist in other metric fields. The Ricci curvature scalar for each space-time is evaluated and used in the determination of true curvature singularities. The Ricci scalar has proved to be very effective in determining the presence of singularities or otherwise in space-time geometry. Results indicate that there are inherent singularities in components of space-time in all three cases. Gravitational singularities in Minkowski space are found to be consequences of the choice of coordinate. Minkowksi space possesses only coordinate singularities and no curvature singularity. This differs with Schwarzschild’s metric which has true curvature singularity. Friedman-Lemaitre-Robertson-Walker (FLRW) and Reissner-Nordstrom metrics have true curvature singularities. Gravitational collapse in the FLRW metric yields a curvature singularity which shows the universe started a finite time ago. Cosmic strings, white holes and blackholes are deduced from the Reissner-Nordstrom singularities. Reissner-Nordstrom solution show that the addition of small amounts of electric charge or angular momentum could completely alter the nature of the singularity, causing the matter to fall through a ‘wormhole’ and emerge into another universe. Analysis of gravitational collapse in this article provides one of the most exciting research frontiers in gravitation physics and high energy astrophysics; as the debate on their physical existence persists.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Gravitational Collapse and Singularities in Some Non-Schwarzschild's Space-Times
    AU  - Chifu Ebenezer Ndikilar
    AU  - Abu Ovansa Samson
    AU  - Hafeez Yusuf Hafeez
    Y1  - 2019/01/07
    PY  - 2019
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    DO  - 10.11648/j.ijass.20180606.11
    T2  - International Journal of Astrophysics and Space Science
    JF  - International Journal of Astrophysics and Space Science
    JO  - International Journal of Astrophysics and Space Science
    SP  - 93
    EP  - 100
    PB  - Science Publishing Group
    SN  - 2376-7022
    UR  - https://doi.org/10.11648/j.ijass.20180606.11
    AB  - Singularities in three non-Schwarzschild space-times: Minkowski, Friedman-Lemaitre-Robertson-Walker and Reissner-Nordstromare investigated. Gravitational collapse in the Schwarzschild solution is obvious and widely studied. However, gravitational collapse should not be limited to Schwarzschild solution only as interesting findings exist in other metric fields. The Ricci curvature scalar for each space-time is evaluated and used in the determination of true curvature singularities. The Ricci scalar has proved to be very effective in determining the presence of singularities or otherwise in space-time geometry. Results indicate that there are inherent singularities in components of space-time in all three cases. Gravitational singularities in Minkowski space are found to be consequences of the choice of coordinate. Minkowksi space possesses only coordinate singularities and no curvature singularity. This differs with Schwarzschild’s metric which has true curvature singularity. Friedman-Lemaitre-Robertson-Walker (FLRW) and Reissner-Nordstrom metrics have true curvature singularities. Gravitational collapse in the FLRW metric yields a curvature singularity which shows the universe started a finite time ago. Cosmic strings, white holes and blackholes are deduced from the Reissner-Nordstrom singularities. Reissner-Nordstrom solution show that the addition of small amounts of electric charge or angular momentum could completely alter the nature of the singularity, causing the matter to fall through a ‘wormhole’ and emerge into another universe. Analysis of gravitational collapse in this article provides one of the most exciting research frontiers in gravitation physics and high energy astrophysics; as the debate on their physical existence persists.
    VL  - 6
    IS  - 6
    ER  - 

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Author Information
  • Physics Department, Federal University Dutse, Dutse, Nigeria

  • Physics Department, Gombe State University, Gombe, Nigeria

  • Physics Department, Federal University Dutse, Dutse, Nigeria

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