## The Painlevé-Gullstrand 'Extension' - A Black Hole Fallacy

**Authors:** Stephen J. Crothers

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.

**Comments:** This paper is published: American Journal of Modern Physics, Volume 5, Issue 1-1 , February 2016, Pages:33-39,

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### Submission history

[v1] 2015-12-03 09:52:42

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