Thunderblog - Guest Contributor Stephen J Crothers
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Black Holes, Unicorns, and All That Stuff


The notion of black holes voraciously gobbling up matter, twisting space-time into contortions that trap light, stretching the unwary into long spaghetti-like strands as they fall inward to ultimately collide and merge with an infinitely dense point-mass singularity, has become a mantra of the scientific community, so much so that even primary school children know about the sinister black hole, waiting patiently, like the Roman child’s Hannibal, for an opportunity to abduct the unruly and the misbehaved. There are almost daily reports of scientists claiming black holes again found here and there.

It is asserted that black holes range in size from micro to mini, to intermediate and on up through to supermassive behemoths. Black holes are glibly spoken of and accepted as scientific facts and that they have been detected at the centre of galaxies. Images of black holes having their wicked ways with surrounding matter are routinely offered with reports of them. Some physicists even claim that black holes will be created in particle accelerators, such as the Large Hadron Collider, potentially able to swallow the Earth, if care is not taken in their production.

Yet despite all this hoopla, contrary to the assertions of the astronomers and astrophysicists of the black hole community, nobody has ever identified a black hole, anywhere, let alone ‘imaged’ one. The pictures adduced to convince are actually either artistic impressions (i.e. drawings) or photos of otherwise unidentified objects imaged by telescopes and merely asserted to be black holes, ad hoc.

No Escape

The alleged signatures of the alleged black hole are an infinitely dense point-mass singularity and an event horizon. Scientists frequently assert that the escape velocity of a black hole (from its event horizon) is that of light and that nothing, not even light, can escape the black hole. In fact, according to the same scientists, nothing, including light, can even leave the event horizon. But there is already a problem with these bald claims (black holes are also alleged to have ‘no hair’).

If the escape velocity of a black hole is that of light, then light, on the one hand, can escape. On the other hand, light is allegedly not able to even leave the event horizon, so the black hole has no escape velocity. If the escape velocity of a black hole is that of light, not only can light both leave and escape, material objects can also leave the event horizon, but not escape, even though, according to the Theory of Special Relativity, they can only have a velocity less than that of light. This just means that material bodies will leave the black hole and eventually stop and fall back to the black hole, just like a ball thrown into the air here on Earth with an initial velocity less than the escape velocity for the Earth. So the properties of the alleged event horizon of a black hole are irretrievably contradictory.

What of the infinitely dense point-mass singularity at the heart of the black hole? It is supposed to be formed by irresistible gravitational collapse so that matter is crushed into zero volume, into a ‘point’, a so-called ‘point-mass’. One recalls from high school that density is defined as the mass of an object divided by the volume of the object. If the mass is not zero and the volume is zero, as in the case of a black hole, one gets division by zero. But all school children know that division by zero is not allowed by the rules of mathematics. Nonetheless, black hole proponents are, by some special privilege, somehow permitted to flout the rules of elementary mathematics and divide by zero! No, the scientists too cannot divide by zero, despite their claims to the contrary.

Einstein Violated

Furthermore, black holes are allegedly obtained from Einstein’s General Theory of Relativity. It is called the General Theory because it is a generalisation of his Special Theory of Relativity. As such, General Relativity cannot, by definition, violate Special Relativity, but that is precisely what the black hole does.

Special Relativity forbids infinite densities because, according to that Theory, infinite density implies infinite energy (or equivalently that a material object can acquire the speed of light in vacuo). Therefore General Relativity too forbids infinite densities. But the point-mass singularity of the black hole is allegedly infinitely dense, in violation of Special Relativity. Thus the Theory of Relativity forbids the existence of a black hole.

Non-event on the Horizon

What now of the event horizon of the black hole? According to the proponents of the black hole it takes an infinite amount of time for an observer to watch an object (via the light from that object, of course) fall into the event horizon. So it therefore takes an infinite amount of time for the observer to verify the existence of an event horizon and thereby confirm the presence of a black hole. However, nobody has been and nobody will be around for an infinite amount of time in order to verify the presence of an event horizon and hence the presence of a black hole. Nevertheless, scientists claim that black holes have been found all over the place.

The fact is nobody has assuredly found a black hole anywhere – no infinitely dense point-mass singularity and no event horizon. Some black hole proponents are more circumspect in how they claim the discovery of their black holes. They instead say that their evidence for the presence of a black hole is indirect. But such indirect ‘evidence’ cannot be used to justify the claim of a black hole, in view of the fatal contradictions associated with infinitely dense point-mass singularities and event horizons. One could just as well assert the existence and presence of deep space unicorns on the basis of such ‘evidence’.

"If the facts don't fit the theory, change the facts." - Albert Einstein

It is also of great importance to be mindful of the fact that no observations gave rise to the notion of a black hole in the first place, for which a theory had to be developed. The black hole was wholly spawned in the reverse, i.e. it was created by theory and observations subsequently misconstrued to legitimize the theory. Reports of black holes are just wishful thinking in support of a belief; not factual in any way.

Another major and fatal contradiction in the idea of the black hole is the allegation that black holes can be components of binary systems, collide or merge. Let us, for the sake of argument, assume that black holes are predicted by General Relativity. The black hole is fundamentally described by a certain mathematical expression called a line-element (which is just a fancy name for a distance formula, like that learnt in high school) that involves just one alleged mass in the entire Universe (just the alleged source of a gravitational field), since the said distance formula is a solution for a space-time allegedly described by Einstein’s equations in vacuum (or, more accurately, emptiness), namely Ric = 0.

One does not need to know anything at all about the mathematical intricacies of this equation to see that it cannot permit the presence of one black hole, let alone two or more black holes. The mathematical object denoted by Ric is what is called a tensor (in this case it is Ricci’s tensor, and hence its notation). The reason why Ric = 0 is because in Einstein’s General Theory of Relativity all matter that contributes to the source of the gravitational field must be described by another tensor, called the energy-momentum tensor. In the case of the so-called vacuum field equations the energy-momentum tensor is set to zero, because there is no mass or radiation present by hypothesis. Otherwise Ric would not be equal to zero. So the alleged black hole can interact with nothing, not even an ‘observer’. Ric = 0 is not a two body situation, only, allegedly, a one body situation (and hence quite meaningless).

One cannot just introduce extra objects into a given solution to Einstein’s field equations, because his theory asserts that the curvature of space-time (i.e. the gravitational field) is due to the presence of matter and that the said matter, all of it, must be described by his energy-momentum tensor. If the energy-momentum tensor is zero, there is no matter present. Einstein's field equations are nonlinear, so the ‘Principle of Superposition’ does not apply. Before one can talk of relativistic binary systems it must first be proved that the two-body system is theoretically well-defined by General Relativity.

This can be done in only two ways:

  • (a) Derivation of an exact solution to Einstein's field equations for the two-body configuration of matter; or

  • (b) Proof of an existence theorem.

There are no known solutions to Einstein's field equations for the interaction of two (or more) masses, so option (a) has never been fulfilled. No existence theorem has ever been proved, by which Einstein's field equations even admit of latent solutions for such configurations of matter, and so option (b) has never been fulfilled either. Since Ric = 0 is a statement that there is no matter in the Universe, one cannot simply insert a second black hole into the space-time of Ric = 0 of a given black hole so that the resulting two black holes (each obtained separately from Ric = 0) mutually interact in a mutual spacetime that by definition contains no matter.

One cannot simply assert by an analogy with Newton's theory that two black holes can be components of binary systems, collide or merge, because the ‘Principle of Superposition’ does not apply in Einstein's theory. Moreover, General Relativity has to date been unable to account for the simple experimental fact that two fixed bodies will approach one another upon release. So from where does the matter allegedly associated with the solution to Ric = 0 come, when this is a statement that there is no matter present? The proponents of the black hole just put it in at the end, a posteriori and ad hoc, in violation of their starting hypothesis that Ric = 0.

No Solution

Finally, the fundamental solution to Ric = 0 is usually called the "Schwarzschild solution". Despite its name, it is not in fact Schwarzschild’s solution. Schwarzschild’s actual solution forbids black holes. The frequent claim that Schwarzschild found and advocated a black hole solution is patently false, as a reading of Schwarzschild’s paper on the subject irrefutably testifies. False too are the claims that he predicted an event horizon and that he determined the "Schwarzschild radius" (i.e. the alleged ‘radius’ of the black hole event horizon). Schwarzschild actually had nothing to do with the black hole, but attaching his name to it lends the notion an additional façade of scientific legitimacy.

Stephen J. Crothers


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Stephen Crothers is a Mathematician and Physicist, and a member of the Santilli-Einstein Academy of Sciences and the Santilli-Galilei Association on Scientific Truth.

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Black Hole - Artist's impression
Artist's impression (cartoon) of a black hole. CREDIT: Dave Smith and

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