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 |
Singularities, Non-Schwarzschild, Reissner-Nordstrom, Curvature, Minkowski, Space-Time
| [1] | Joshi P. and Malafarina D. (2012). Recent Developments in Gravitational Collapse andSpacetime Singularities. International Journal of Modern Physics D, 20(14) 2641-2729. |
| [2] | Curiel, E. (1999). The Analysis of Singular Spacetime. Philosophy of Science, 66: , 119-145. |
| [3] | Joshi P. S., (2000). Gravitational Collapse: The Story so far. Pramana-J Phys, 55(4), 529-544. |
| [4] | Hawking, S. W., and Penrose, R. (1970). The Singularities of Gravitational Collapse and Cosmology. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 314, 1519, 529-548. |
| [5] | Curiel E and Bokulich, P. (2009). Singularities and Blackholes. Retrieved on 4th, March, 2015. http://www.google.com.ng/url?q=http://plato.stanford. |
| [6] | Ndikilar C. E. and S. X. K Howusu (2009); Gravitational Radiation and Propagation Field Equation Exterior to Astrophysically Real or Hypothetical Time Varying Distributions of Mass within Regions of Spherical Geometry", Physics Essays 22(1): 73-77. |
| [7] | Hawking, S. (2014). Singularities and the geometry of spacetime. The European Physical Journal H, 39(4), 413-503. |
| [8] | Mohajan H. (2013). Friedman, Robertson-Walker Models in Cosmology. Journal ofEnvironmental Treatment Techniques 1(3) 158-164. |
| [9] | Carroll S. M. (2004) Spacetime and Geometry: An introduction to general relativity. Adison Wesley, London, United Kingdom. 48-92. |
| [10] | Griffiths, J. B., and Podolski, J. (2009). Exact Space-Times in Einstein’s General Relativity. Cambridge, United Kingdom: Cambridge University Press (Virtual Publishing). |
| [11] | Penrose R. (1965). Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14:57–59. |
| [12] | Henry C. R., (1999). Kretschmann Scalar for a Kerr-Newman Blackhole. Arxiv:astro. ph 1(1) 5-8. |
| [13] | Ndikilar C. E., A. Usman and O. C Meludu (2011); General Relativistic Theory of Oblate Spheroidal Gravitational Fields, The African Review of Physics 6:193 – 202. |
| [14] | Anderson, L. D., (2012). Cosmic string time travel. Retrieved Dec. 5 2016 fromhttp://www.andersoninstitute.com/cosmicstrings.html. |
| [15] | Sakellariadou M. (2009). Cosmic Strings and Cosmic Superstrings. Arxiv:0902.0569 2 6-10. |
| [16] | Frolov V. P., and Fursaev, D. V., (2001). Mining energy from a blackhole by strings. Arxiv: hep-th/0012260 5 6-11. |
| [17] | Ndikilar C. E. (2012); Gravitational Fields Exterior to Homogeneous Spheroidal Masses, Abraham Zelmanov Journal of General Relativity, Gravitation and Cosmology 5:31 – 67. |
| [18] | Schmidt, B. P. (2012). Nobel lecture: Accelerating expansion of the Universe through observations of distant supernovae. Reviews of Modern Physics 84, 1151-1163. |
| [19] | Ndikilar C. E. and Nasir M. M. (2016). Elementary Space Science. Ahmadu Bello University Press Limited, Zaria, Kaduna state, Nigeria. |
| [20] | Stoica O. C (2015). The Geometry of singularities and the black hole informationparadox. Journal of Physics: Conference Series, 626, 012028. |
| [21] | Curiel, E. (2009). General relativity needs no interpretation. Philosophy of Science 76, 44–72. |
| [22] | Cattoen, C. and Visser, M. (2005). Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities, and extremality events. Classical and QuantumGravity 22, 4913. |
| [23] | Zinkernagel H., (2008). Did time have a beginning? International Studies in the Philosophy of Science 22(3), 237-258. |
| [24] | Heinicke, C., and Hehl F. W. (2015), “Schwarzschild and Kerr Solutions of Einstein's Field Equation - An Introduction. International Journal of modern Physics D, 24(02), 134-138. |
| [25] | Redd N. T. (2015). Worm holes: Science and astronomy. Retrieved from www.Space.com. 6th November, 2016. |
| [26] | Lam, V. (2007). The singular nature of spacetime. Philosophy of Science 74 (5), 712-723. |
| [27] | Joshi, P. S. (2002). Cosmic Censorship: A Current Perspective, Modern Physics Letters A, 17: 1067-1079. |
| [28] | Hawking, S. (1971). Gravitationally collapsed objects of very low mass. Monthly Notices of the Royal Astronomical Society, 152(1), 75-78. |
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
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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Download@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}
}
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 N1 - https://doi.org/10.11648/j.ijass.20180606.11 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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