by

Stephen J. Crothers

William D. Clinger has posted a webpage
in which he cites himself and others as sources of mathematical refutations of my proofs that the theory of black holes is false.
Clinger asserts that I have committed ''*mathematical errors*'', and provides a list of critics besides himself that he says
''*Crothers has been unable to answer*''. However, his charge is patently false as I had already answered three of the four critics Clinger listed.
I have now answered all of them, including Clinger.

The first on Clinger's list is Gerardus 't Hooft, Nobel Laureate (Physics). I had dealt with 't Hooft's '*Strange Misconceptions*'
here.

The second on Clinger's list is Gerhard W. Bruhn. I had dealt with Bruhn here.

Third on Clinger's list is Jason J. Sharples, an Associate Professor of applied mathematics at the University of New South Wales, Australian Defence Force Academy. Clinger cites three articles by Sharples:

(a) Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers

(b) On Crothers' counter-examples to the Kruskal-Szekeres extension

(c) Watching the World Cup

I had answered Sharples' first article above long ago, here. As for Sharples' other two articles, I have answered them here and here respectively.

The fourth critic on Clinger's list is Christian C. Corda. Clinger cited Corda with the following remarks:

''*Christian Corda has published
a clarification on the debate on "the original Schwarzschild solution".
I cited this paper
in my thread because it covers most of the same ground in much greater technical detail.*''

In my two responses to Corda, here and here, I revealed
that Corda's 'analysis' is nothing but a copy of the work of Karl Schwarzschild (1916). Corda reproduced Schwarzschild's derivation of the latter's
solution to Einstein's field equations in the absence of matter, point by point, by merely altering Schwarzschild's symbols, renumbering Schwarzschild's numbered
equations, numbering Schwarzschild's un-numbered equations, and changing the order of terms in Schwarzschild's equations. Thus, Corda has added
nothing new to the subject matter. Clinger failed to realise that Corda's 'analysis', ''*in much greater technical detail*'' is a farce, by
virtue of it being nothing but a copy of Schwarzschild. Schwarzschild's solution does not permit a black hole. One can only wonder why Corda
copied Schwarzschild and offered it as a 'peer-reviewed' new 'analysis' that proves the mathematical theory of black holes.
Clinger's failure to notice that Corda copied Schwarzschild speaks for itself, as does the 'peer review' and publication
of Corda's article by the *Electronic Journal of Theoretical Physics*. That Clinger also cites the absurd 'rationalwiki' website as a
source also speaks for itself.

In any event, there is no escape from the fact that the mathematical theory of black holes violates the rules of pure mathematics, and is thereby certainly false, as I explained again some time ago, for instance, in my response to critics here and here. Moreover, Clinger relies upon the Painleve-Gullstrand 'extension' to justify the black hole. However, the Painleve-Gullstrand method does not produce a black hole, except by means of the very same volations of the rules of pure mathematics:

Crothers, S.J., The Painleve-Gullstrand 'Extension' - A Black Hole Fallacy, *American Journal of
Modern Physics*, 5, Issue 1-1, February 2016, Pages:33-39

My email address: thenarmis@yahoo.com

Page established: 6^{th} May 2016