2020, Volume 9
2019, Volume 8
2018, Volume 7
2017, Volume 6
2016, Volume 5
2015, Volume 4
2014, Volume 3
2013, Volume 2
2012, Volume 1

Volume 5, Issue 1-1, February 2016, Page: 33-39
The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy
Stephen J. Crothers, Alpha Institute of Advanced Study, Brisbane, Australia
Received: Aug. 9, 2015;       Accepted: Aug. 19, 2015;       Published: Oct. 20, 2015
DOI: 10.11648/j.ajmp.s.2016050101.15      View  5431      Downloads  147
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.
General Relativity, Black Hole, Metric Extensions, Ricci Tensor, Escape Velocity
To cite this article
Stephen J. Crothers, The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy, American Journal of Modern Physics. Special Issue: Physics Without Higgs and Without Supersymmetry. Vol. 5, No. 1-1, 2016, pp. 33-39. doi: 10.11648/j.ajmp.s.2016050101.15
Crothers, S. J., On the General Solution to Einstein’s Vacuum Field and Its Implications for Relativistic Degeneracy, Progress in Physics, v.1, pp.68-73, 2005, _files/2005/PP-01-09.PDF.
Crothers, S. J., General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate,
Crothers, S. J., On the Generation of Equivalent ‘Black Hole’ Metrics: A Review, American Journal of Space Science, 2015,,
Crothers, S. J., On the ‘Stupid’ paper by Fromholz, Poisson and Will,
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,
Schwarzschild, K., On the Gravitational Field of a Point Mass According to Einstein's Theory, Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl: 189 (1916),
Droste, J., The field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that field, Ned. Acad. Wet., S.A., v. 19, 197, 1917,
Abrams, L. S., Black holes: the legacy of Hilbert's error, Can. J. Phys., v. 67, 919, 1989,
Dictionary of Geophysics, Astrophysics, and Astronomy, Matzner, R. A., Ed., CRC Press LLC, Boca Raton, LA, 2001, _of _geophysics_astro.html.
Brillouin, M., The singular points of Einstein's Universe. Journ Phys. Radium, v. 23, 43, 1923,
Fromholz, P., Poisson, E., Will, C., The Schwarzschild metric: It's the coordinates, stupid! 2 Aug. 2013, arXiv:1308.0394v1 [gr-qc].
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,
Einstein, A., The Meaning of Relativity, expanded Princeton Science Library Edition, 2005.
McMahon, D., Relativity Demystified, A Self teaching Guide, McGraw-Hill, New York, 2006.
Tolman, R. C., Relativity Thermodynamics and Cosmology, Dover Publications Inc., New York, 1987.
d’Inverno, R., Introducing Einstein’s Relativity, Oxford University Press, 1992.
Eddington, A. S., The mathematical theory of relativity, Cambridge University Press, Cambridge, 2nd edition, 1960.
Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General theory of Relativity, John Wiley & Sons, Inc., 1972.
Crothers, S. J., To Have and Not to Have - the Paradox of Black Hole Mass, 12 August, 2015,
Crothers, S. J., A Few Things You Need to Know to Tell if a Nobel Laureate is Talking Nonsense, 10 July 2015,
Crothers, S. J., Black Hole Escape Velocity - a Case Study in the Decay of Physics and Astronomy,
Crothers, S. J., On Isotropic Coordinates and Einstein’s Gravitational Field, Progress in Physics, v.3, pp.7-12, 2006,
Crothers, S. J., A Nobel Laureate Talking Nonsense: Brian Schmidt - a Case Study, 16 July, 2015,
Frazer, J. G., The Golden Bough, (A new abridgement), Oxford University Press, Oxford, 2009.
Robitaille, P.-M., Crothers, S. J., “The Theory of Heat Radiation” Revisited: A Commentary on the Validity of Kirchhoff’s Law of Thermal Emission and Max Planck’s Claim of Universality, Progress in Physics, v. 11, p.120-132, 2015,
Browse journals by subject