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 that have been published by Stephen J Crothers.

Consider, for example,

Stephen J Crothers. Gravitation on a spherically symmetric metric manifold. Progress in Physics 2, April 2007, pages 68-74. http://www.ptep-online.com/index_files/2007/PP-09-14.PDF

Here are the topic sentences of that paper's last two paragraphs:

Stephen J Crothers:

Black holes are not predicted by General Relativity....

It follows in similar fashion that expansion of the Universe and the Big Bang cosmology are inconsistent with General Relativity, as is easily demonstrated [24, 25].

Crothers is making a purely mathematical claim. He isn't talking about whether black holes actually exist or the Big Bang ever happened. He's saying the mathematical theory of general relativity predicts neither, and is inconsistent with both.

In this thread, we will consider that purely mathematical question. We will accept the general theory of relativity as a given, even though many physicists hope GR will ultimately be replaced by an even better theory that doesn't break down at the singularities. We will analyze the mathematical arguments put forth by Crothers and a few others, and we will identify some of the mathematical errors that Crothers has made. We will also construct mathematical counter-examples to some of his arguments.

According to Crothers, the truth about black holes is being suppressed:

Stephen J Crothers:

Neither the layman nor the specialist, in general, have any knowledge of the historical circumstances underlying the genesis of the idea of the Black Hole. Essentially, almost all and sundry simply take for granted the unsubstantiated allegations of some ostentatious minority of the relativists. Unfortunately, that minority has been rather careless with the truth and is quite averse to having its claims corrected, notwithstanding the documentary evidence on the historical record. Furthermore, not a few of that vainglorious and disingenuous coterie, particularly amongst those of some notoriety, attempt to dismiss the testimony of the literature with contempt, and even deliberate falsehoods, claiming that history is of no importance. The historical record clearly demonstrates that the Black Hole has been conjured up by combination of confusion, superstition and ineptitude, and is sustained by widespread suppression of facts, both physical and theoretical....

Although that's the sort of language we see more often at JREF than in a scientific journal, those were the opening words of the abstract for

Stephen J Crothers. A brief history of black holes. Progress in Physics 2, April 2006, pages 54-57. http://www.ptep-online.com/index_files/complete/PiP-2006-02.pdf

Crothers's papers are rife with errors. Many of those errors have already been pointed out by Jason J Sharples, and I will explain some other errors later on in this thread.

Crothers started with and was inspired by a paper that's harder to dismiss:

Leonard S Abrams. Black holes: the legacy of Hilbert's error. Canadian Journal of Physics 67, 1989, page 919ff. http://arxiv.org/abs/gr-qc/0102055

That paper is very well-written, and its math is almost (but not quite!) correct.

That paper's central error is topological. I think I can explain that topological error to non-mathematicians. That explanation may also interest the physicists who know Abrams's conclusion was wrong but don't know exactly where he went wrong.

Related threads

This thread is related to three recent or ongoing threads:

I didn't want to derail any of those threads with this mathematical side-show. The "Black holes" thread is about the mainstream theory of black holes, not the crackpot EU denial of black holes. The third thread listed is about the recent publication of EU pseudoscience in a particular journal; none of the papers I intend to discuss were published in that journal.

In this thread, I hope we can maintain our focus on the mathematics. To reduce redundancy, I will occasionally link to math that's already been posted in one of the above threads.


This is an HTML translation of something I wrote in March 2012 concerning the mathematics of black hole denialism at the online forum now known as the Internation Skeptics Forum. The original forum posts are still online, but that forum no longer renders equations (LaTeX) correctly. For this translation to HTML, I have replaced LaTeX by images and made a few small corrections and deletions. For context and an index, see my introduction to this material.


Last updated: 25 June 2015.

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