## Counter-Examples to the Kruskal-Szekeres Extension: In Reply to Jason J. Sharples

**Authors:** Stephen J. Crothers

Jason J. Sharples of the University of New South Wales wrote an undated article titled ‘On Crothers’ counter-examples to the Kruskal-Szekeres extension’, in which he asserted, “The claims relating to the counter-examples made by the author in [1] about the invalidity of the Kruskal-Szekeres extension and the Schwarzschild black hole are completely erroneous.” However, Sharples failed to understand the arguments I adduced and consequently committed serious errors in both mathematics and physics. In his endeavour to prove me ‘erroneous’, Sharples introduced what he calls “an inverted radial coordinate”. Contrary to Sharples’ allegation, there is no ‘inverted radial coordinate’ involved. Sharples simply failed to comprehend the geometry of the problem. Sharples’ mathematical proof that I am ‘erroneous’ violates the rules of pure mathematics. The Kruskal-Szkeres extension and the Schwarzschild black hole it facilitates are fallacious because they violate the rules of pure mathematics.

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### Submission history

[v1] 2016-04-21 11:33:27

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