Mathematics of Black Hole Denialism
According to the Electric Universe folk at the Thunderbolts web site, black holes do not exist. According to the EU folk, black holes are not even consistent with Einstein's general theory of relativity.
As intellectual cover for their position, the EU folk cite a series of papers written by Stephen J Crothers that purport to provide mathematical proof of this claim:
Stephen J Crothers:
...expansion of the Universe and the Big Bang cosmology are inconsistent with General Relativity, as is easily demonstrated [24, 25].
In a thread I started at what is now the International Skeptics Forum (ISF), I analyzed the mathematical arguments put forth by Crothers and a few others, identifying some of the mathematical errors Crothers has made and constructing mathematical counterexamples to some of his arguments. That forum's software no longer renders LaTeX correctly, making the thread's equations unreadable. I have therefore translated my contributions to that thread into the HTML hosted here:
 introduction
 topology
 Leonard S Abrams
 mental baggage
 a manifold that extends the manifold Crothers claims cannot be extended
 a basic misunderstanding of manifolds
 several details are wrong as well
 Crothers cites his erroneous papers as proof black holes "are not predicted by General Relativity at all"
 summary of a counterexample to the central claim made by Crothers
 the radial coordinate r is not a Euclidean radius
 Contra Crothers, the relativists have known that for 40 years
Near the end of that thread, another member of the forum explained why intelligent people cannot think rationally about certain topics.
Spamming
Crothers has begun to send spam emails promoting his views and attacking his critics. He claims to "have dealt thoroughly" with their criticisms, but he is just repeating his mistakes while insisting his critics are wrong.
Refutations
Here are some of the criticisms Crothers has been unable to answer:
 Gerard 't Hooft, who won a Nobel Prize in 1999, has written about several strange misconceptions of general relativity, including some promoted by a "Mr. C" and his friends.
 In 2008, Gerhard W Bruhn wrote a Discussion of S. Crothers' Views on Black Hole Analysis in GRT that refutes the two main claims made by Mr Crothers. Bruhn's refutation was ignored by the journal in which Crothers has published the great majority of his papers.

Jason J Sharples, a professor of applied mathematics, has
written several articles that explain some of the mistakes
being made by Crothers:
 Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers
 On Crothers' counterexamples to the KruskalSzekeres extension
 Watching the World Cup
 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.
RationalWiki's article on Mr Crothers summarizes his career and claims.