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The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy

Received: 9 August 2015     Accepted: 19 August 2015     Published: 20 October 2015
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Abstract

A number of methods have been employed by cosmologists to effect what they call an ‘extension’ of their ‘Schwarzschild solution’, to remove the singularity at their ‘Schwarzschild radius’ rs = 2Gm/c^2; the latter they maintain is the radius of the ‘event horizon’ of a black hole. They call the singularity at the Schwarzschild radius a coordinate singularity. The method of extension most often employed by cosmologists is the Kruskal-Szekeres extension, but sometimes the Painlevé-Gullstrand extension is used. The quantity r appearing in all these metrics is invariably treated by cosmologists as the radial distance, most evident in their ‘Schwarzschild radius’. Intuitively, radial distance is ≥ 0 and so, on their false assumption that r is the radial distance in the ‘Schwarzschild solution’, the cosmologists seek to drive it down to zero where they say there is a physical singularity. Although cosmologists have devised mathematical-like methods to seemingly do this, to produce their black hole, all their methods violate the rules of pure mathematics and so they are inadmissible. Consequently, the Painlevé-Gullstrand ‘extension’ is invalid. Moreover, since material sources cannot be both present in and absent from Einstein’s field equations by the very same mathematical constraint, the whole theory of black holes is fallacious.

Published in American Journal of Modern Physics (Volume 5, Issue 1-1)

This article belongs to the Special Issue Physics Without Higgs and Without Supersymmetry

DOI 10.11648/j.ajmp.s.2016050101.15
Page(s) 33-39
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), 2015. Published by Science Publishing Group

Keywords

General Relativity, Black Hole, Metric Extensions, Ricci Tensor, Escape Velocity

References
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[4] Crothers, S. J., On the ‘Stupid’ paper by Fromholz, Poisson and Will, http://vixra.org/pdf/1310.0202.pdf.
[5] Crothers, S. J., A Few Things You Need to Know to Tell if a Mathematical Physicist is Talking Nonsense: the Black Hole - a Case Study, 29 July, 2015, http://vixra.org/pdf/1508.0007v1.pdf.
[6] Schwarzschild, K., On the Gravitational Field of a Point Mass According to Einstein's Theory, Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl: 189 (1916), http://arxiv.org/pdf/physics/9905030v1.
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[18] Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General theory of Relativity, John Wiley & Sons, Inc., 1972.
[19] Crothers, S. J., To Have and Not to Have - the Paradox of Black Hole Mass, 12 August, 2015, http://vixra.org/pdf/1508.0106v1.pdf.
[20] Crothers, S. J., A Few Things You Need to Know to Tell if a Nobel Laureate is Talking Nonsense, 10 July 2015, http://vixra.org/pdf/1507.0067v2.pdf.
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  • APA Style

    Stephen J. Crothers. (2015). The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy. American Journal of Modern Physics, 5(1-1), 33-39. https://doi.org/10.11648/j.ajmp.s.2016050101.15

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    Stephen J. Crothers. The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy. Am. J. Mod. Phys. 2015, 5(1-1), 33-39. doi: 10.11648/j.ajmp.s.2016050101.15

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    AMA Style

    Stephen J. Crothers. The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy. Am J Mod Phys. 2015;5(1-1):33-39. doi: 10.11648/j.ajmp.s.2016050101.15

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  • @article{10.11648/j.ajmp.s.2016050101.15,
      author = {Stephen J. Crothers},
      title = {The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy},
      journal = {American Journal of Modern Physics},
      volume = {5},
      number = {1-1},
      pages = {33-39},
      doi = {10.11648/j.ajmp.s.2016050101.15},
      url = {https://doi.org/10.11648/j.ajmp.s.2016050101.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2016050101.15},
      abstract = {A number of methods have been employed by cosmologists to effect what they call an ‘extension’ of their ‘Schwarzschild solution’, to remove the singularity at their ‘Schwarzschild radius’ rs = 2Gm/c^2; the latter they maintain is the radius of the ‘event horizon’ of a black hole. They call the singularity at the Schwarzschild radius a coordinate singularity. The method of extension most often employed by cosmologists is the Kruskal-Szekeres extension, but sometimes the Painlevé-Gullstrand extension is used. The quantity r appearing in all these metrics is invariably treated by cosmologists as the radial distance, most evident in their ‘Schwarzschild radius’. Intuitively, radial distance is ≥ 0 and so, on their false assumption that r is the radial distance in the ‘Schwarzschild solution’, the cosmologists seek to drive it down to zero where they say there is a physical singularity. Although cosmologists have devised mathematical-like methods to seemingly do this, to produce their black hole, all their methods violate the rules of pure mathematics and so they are inadmissible. Consequently, the Painlevé-Gullstrand ‘extension’ is invalid. Moreover, since material sources cannot be both present in and absent from Einstein’s field equations by the very same mathematical constraint, the whole theory of black holes is fallacious.},
     year = {2015}
    }
    

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  • Alpha Institute of Advanced Study, Brisbane, Australia

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