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

Stephen J. Crothers

doi:doi:10.11648/j.ajmp.s.2016050101.15

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

Stephen J. Crothers

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

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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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ACS 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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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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TY  - JOUR
T1  - The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy
AU  - Stephen J. Crothers
Y1  - 2015/10/20
PY  - 2015
N1  - https://doi.org/10.11648/j.ajmp.s.2016050101.15
DO  - 10.11648/j.ajmp.s.2016050101.15
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 33
EP  - 39
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.s.2016050101.15
AB  - 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.
VL  - 5
IS  - 1-1
ER  -

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Author Information

Stephen J. Crothers

Alpha Institute of Advanced Study, Brisbane, Australia

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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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ACS 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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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy
AU  - Stephen J. Crothers
Y1  - 2015/10/20
PY  - 2015
N1  - https://doi.org/10.11648/j.ajmp.s.2016050101.15
DO  - 10.11648/j.ajmp.s.2016050101.15
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 33
EP  - 39
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.s.2016050101.15
AB  - 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.
VL  - 5
IS  - 1-1
ER  -

Copy | Download