by

Stephen J. Crothers

The first step to understanding the issues is to see that black hole theory and big bang theory are contradictory and therefore mutually exclusive. A black hole universe and a big bang universe cannot coexist. The simplest way to see this is by merely comparing the list of generic defining characteristics of black hole universes and big bang universes.

**All alleged black hole universes:**

(1) are spatially infinite

(2) are eternal

(3) contain only one mass

(4) are not expanding

(5) are either asymptotically flat or asymptotically curved.

**The alleged big bang universes:**

(1) are spatially finite (one case) or spatially infinite (two cases)

(2) are of finite age

(3) contain radiation and many masses, including multiple black holes (some of which are primordial)

(4) are expanding

(5) are not asymptotically anything.

A simple comparison of the two lists immediately reveals that the black hole and the big bang are defined very differently. The defining features of the black hole contradict the defining features of the big bang. Consequently the black hole and the big bang are mutually exclusive. No mathematics is required to see this because it is a matter of elementary logic.

The terms asymptotically flat and asymptotically curved need perhaps a few more words of explanation. Asymptotically flat simply means that with
increasing radial distance from the black hole the alleged *infinite* spacetime curvature at its singularity changes and gets closer and closer to zero
(i.e. flatness). Asymptotically curved simply means that with increasing radial distance from the black hole the alleged *infinite* spacetime
curvature at its singularity changes and gets closer and closer to a finite non-zero value (i.e. to some curved spacetime such as anti-de Sitter spacetime).
The spacetimes of all alleged types of big bang universes are not asymptotically anything.

Now, upon what set of Einstein's field equations and upon what solution thereto do the proponents of the black hole and the big
bang rely for multiple black holes in an expanding big bang universe that is of finite age and is not asymptotically anything? None! They have
no such set of field equations let alone a solution. They simply *superpose* black hole universes upon big bang universes and generally don't even
specify which type of black hole universe and which type of big bang universe they superpose. In this way the black hole big bang universe is
arbitrarily manufactured.

The types of black hole alleged are: (1) non-rotating, electric charge neutral; (2) non-rotating, and electrically charged; (3) rotating, and electric charge neutral; (4) rotating, and electrically charged.

There are three alleged types of big bang universe: (1) spatially finite (constant positive spacetime curvature); (2) spatially infinite (flat - or otherwise of zero spacetime curvature); (3) spatially infinite (constant negative spacetime curvature).

__THE PRINCIPLE OF SUPERPOSITION__

Einstein's field equations are *nonlinear*. Consequently the Principle of Superposition is invalid in General Relativity. One cannot therefore
superpose any alleged black hole universe upon any alleged big bang universe or upon any other alleged black hole universe. Similarly one cannot
superpose any alleged big bang universe upon any alleged black hole universe or upon any other alleged big bang universe. One cannot superpose
any matter and radiation onto any black hole universe or big bang universe in order to get stars and galaxies and accretion discs and jets and
planets and multiple black holes, etc. To do so violates the mathematical structure of General Relativity. However, superposition is precisely
how the astrophysical scientists have generated their big bang universe with its multiple black holes and stars and galaxies etc. It is easy to
express this mathematically. Let ** X** and

Upon what set of Einstein's field equations and upon what solution thereto do the proponents of the black hole and big bang rely for black holes and dark companions in binary and other systems (e.g. Sgr A*) in an expanding big bang universe? None! They just superpose.

__SOME EXAMPLES__

Professor Joss Bland-Hawthorn, Dr. Ralph Sutherland, Dr. Phil Maloney and Astronomer Royal Professor Martin Rees are quoted in the following University of Sydney online news article:

They talk of a supermassive black hole at Sgr A* (the centre of the Milky Way) that allegedly erupted some 2 million years ago with a huge emission of radiation. Professor Bland-Hawthorn is quoted in the article thus:

"*The realisation that these black holes can switch on and off within a million years, which given the universe is 14 billion years old means
very rapidly, is a significant discovery.*"

"*There are lots of stars and gas clouds that could fall onto the hot disk around the black hole.*"

Astronomer Royal Professor Martin Rees is quoted in the article thus:

"*It's been long suspected that our Galactic Centre might have sporadically flared up in the past. These observations are a highly suggestive
smoking gun.*"

Furthermore,

"*Black holes, the most remarkable consequences of Einstein’s theory, are not just theoretical constructs. There are huge numbers of them in
our Galaxy and in every other galaxy, each being the remnant of a star and weighing several times as much as the Sun. There are much larger ones,
too, in the centers of galaxies. Near our own galactic center, stars are orbiting ten times faster than their normal speeds within a galaxy. *"

[Martin Rees, Our Cosmic Habitat (2001)]

Upon what set of Einstein field equations and upon what solution thereto do they all rely for the "*lots of stars and gas clouds that could
fall onto the hot disk around the black hole*" at "*our Galactic Centre*" in an expanding big bang universe that is "*14 billion years
old*"? None!

What type of black hole do they allege at Sgr A*? They don't tell us in the above online report. Is it rotating or not, is it charged or not?

The singularity of the alleged non-rotating black hole is a mathematical point – it has no extension and hence no volume, but it allegedly has mass (and infinite density). The singularity of the alleged rotating black hole is the circumference of a circle; not a circle mind you, only the circumference of a circle. It too has no volume, but allegedly has mass (and infinite density).

"*… there must be a singularity of infinite density, within the black hole.*"

[Hawking, S. W., The Theory of Everything, The Origin and Fate of the Universe, New Millennium Press, Beverly Hills, CA,
(2002)]

The big bang universes have a very peculiar nature:

"*One crucial assumption underlies the standard hot big-bang model: that the universe 'began' in a state of rapid expansion from a very nearly
homogeneous, isotropic condition of infinite (or near infinite) density and pressure.*"

[Misner, C. W., Thorne, K. S., Wheeler, J. A., Gravitation, W. H. Freeman and Company, New York, (1970)]

Now I ask you dear reader, how close to infinite must one get to be "*near infinite*"?

Misner, Thorne and Wheeler are not the only to propose such "*near infinite*" nonsense. It is quite standard fare for the proponents of
black holes and big bangs.

"*But is that, in fact, because of discovering that empty space has energy, it seems quite plausible that our universe may be just one
universe in what could be almost an infinite number of universes and in every universe the laws of physics are different and they come into
existence when the universe comes into existence.*"

[Krauss, L., A Show About Nothing, Q&A, television station ABC1, Australia, (Monday, 18 February, 2013a)]

I ask you, dear reader, just how close to infinite must one get to attain "*almost an infinite number*"? This is little different to the
"*near infinite*" density and pressure of Misner, Thorne and Wheeler, and Hawking's infinite hotness of nothingness:

"*At the big bang itself, the universe is thought to have had zero size, and to have been infinitely hot.*"

[Hawking, S. W., A Brief History of Time from the Big Bang to Black Holes, Transworld Publishers Ltd., London, (1988)]

Professor Joss Bland-Hawthorn speaks about his 'research' in this Youtube presented interview:

In this interview Bland-Hawhtorn talks of black hole escape velocity. He even says that the escape velocity of a black hole is the speed of light. If the escape velocity of a black hole is that of light, as Bland-Hawthorn claims, along with all the other proponents of the black hole, then light, by the very definition of escape velocity, can leave and escape from the black hole. However, on the one hand it is claimed by the astrophysical mathemagicians that the black hole has an escape velocity:

"* black hole A region of spacetime from which the escape velocity exceeds the velocity of
light.*"

[Dictionary of Geophysics, Astrophysics and Astronomy, 2001]

"* black hole A massive object so dense that no light or any other radiation can escape from it;
its escape velocity exceeds the speed of light.*"

[Collins Encycloaedia of the Universe, Harper Collins Publishers, London, 2001]

Yet on the other hand it is also claimed that nothing can even *leave* a black hole:

"*I had already discussed with Roger Penrose the idea of defining a black hole as a set of events from which it is not possible to escape to a
large distance. It means that the boundary of the black hole, the event horizon, is formed by rays of light that just fail to get away from the
black hole. Instead, they stay forever hovering on the edge of the black hole.*"

[Hawking, S. W., The Theory of Everything, The Origin and Fate of the Universe, New Millennium Press, Beverly Hills, CA, (2002)]

"*The problem we now consider is that of the gravitational collapse of a body to a volume so small that a trapped surface forms around it;
as we have stated, from such a surface no light can emerge.*"

[Chandrasekhar, S., The increasing role of general relativity in astronomy, *The Observatory*, 92, 168, (1972)]

Thus, the black hole is alleged to have an escape velocity and not to have an escape velocity simultaneously, which is impossible.

Upon what set of Einstein field equations and upon what solution thereto do the astrophysical mathemagicians rely for black hole escape velocity, bearing in mind that all alleged black hole universes contain only one mass whereas escape velocity is a two-body relation: one body escapes from another body, where there is no restriction placed upon the finite magnitude of the mass of either body?

Go here for the email exchange between me, Professor Bland-Hawthorn et al, and Professor John Friedman.

__BLACK HOLES EVAPORATE?__

Hawking would have us believe that the black hole not only exists in multitudes but disappears by quantum-mechanical evaporation. So according to Hawking the black hole universes are not eternal; they are non-static universes. If so then a black hole universe transmutes into a non-black hole universe. What universe is that? Hawking has no set of Einstein field equations for a universe containing only Hawking radiation and hence no solution thereto. Moreover, Hawking maintains that his Hawking radiation universe exists in black hole universes that contain lots of black holes because he alleges black holes all over the place, just as all the proponents of the black hole do, all in some expanding big bang universe (and which big bang universe do they rely upon?). Hawking applies quantum mechanics to universes that are by definition eternal (static).

In his interview Professor Bland-Hawthorn presented cartoons for visual impact and impression upon his audience and said that the alleged supermassive black hole Sgr A* has been growing since the (nondescript) big bang spawned the Universe. This black hole must therefore be a primordial black hole, not formed by the 'collapse' of a star, and it has not only grown all this time (14 billion years), it has not 'evaporated' into Hawking radiation to transmute thereby a black hole universe superposed upon many other black hole universes and stellar universes all in turn superposed upon some big bang universe, turning into some non-black hole, non-big bang universe for which no Einstein field equations have been furnished, let alone a solution thereto.

__MATTER FALLING INTO BLACK HOLES?__

The astrophysical mathemagicians tell us that they can observe matter outside the event horizons of their black holes. This alleged matter comes not from any alleged solution to Einstein's field equations for any type of black hole. They just put it into their black hole universe by superposition, and have added to their black hole, again by superposition, The Milky Way, and all the rest of the matter in the Universe, despite the facts that all alleged black hole universes contain only one mass, are eternal, are not expanding, cannot coexist with themselves or any big bang universe because their defining characteristics contradict one another, and that the Principle of Superposition is invalid in General Relativity.

__BIG BANG UNIVERSES CONTAIN LOTS OF RADIATION, BLACK HOLES, STARS AND GALAXIES?__

All three alleged types of big bang universe are one-mass models because they all treat the Universe as being completely filled by a single continuous homogeneous distribution of matter of uniform macroscopic density and pressure. The astrophysical mathemagicians do this because there are no known Einstein field equations for two or more masses, let alone solutions thereto, and no existence theorem by which it can even be asserted that Einstein's field equations contain latent solutions for two or more masses. General Relativity can't even account for the simple experimental fact that two stationary suspended bodies approach one another upon release. Concerning this uniform density and pressure,

"*… it must be remembered that these quantities apply to the idealized fluid in the model, which we have substituted in place of the matter
and radiation actually present in the real universe.*"

[Tolman, R. C., Relativity Thermodynamics and Cosmology, Dover Publications Inc., New York, (1987)]

"*We may, however, introduce a more specific hypothesis by assuming that the material filling the model can be treated as a
perfect fluid.*"

[Tolman, R. C., Relativity Thermodynamics and Cosmology, Dover Publications Inc., New York, (1987)]

"*We can then treat the universe as filled with a continuous distribution of fluid of proper macroscopic density ρ _{oo} and
pressure p_{o}, and shall feel justified in making this simplification since our interest lies in obtaining a general framework for the
behaviour of the universe as a whole, on which the details of local occurrences could be later superposed.*"

[Tolman, R. C., Relativity Thermodynamics and Cosmology, Dover Publications Inc., New York, (1987)]

Superposed? Superposition is invalid in General Relativity. The astrophysical mathemagicians just apply superposition to manufacture their black hole big bang universes, thereby violating the mathematical principles of General Relativity and the very definitions of the models they employ.

They also clutch at *approximations*. Einstein and his followers approximate his field equations by means of *linearisation* of
his field equations. Recall that Einstein's field equations are nonlinear. With this *linearisation* they generate all sorts of stuff,
including Einstein's alleged gravitational waves. These Einstein gravitational waves are supposedly caused by black holes interacting with one another
and with other matter. But all alleged black hole universes not only contain only one mass, they are obtained from Einstein's nonlinear field
equations, not from the so-called 'linearised' field equations. So linear universes are also superposed upon nonlinear universes. All the
astromathemagicians are now very happy. Drinks all round. They have managed to deceive not only their audience but also themselves!

Page established: 29^{th} December 2014