Stephen Crothers

• Alpha Institute of Advanced Study

It has been critically argued by V. A. Leus (Sobolev Institute of Mathematics, Novosibirsk, Russia) that in my proof that Einstein’s Special Theory of Relativity is logically inconsistent and therefore false, I violated the basic tenets of Special Relativity and foisted an alternative theory upon Einstein’s. A careful study of the critical analysis...

Einstein's method of synchronizing clocks in his special theory of relativity is inconsistent with the Lorentz transformation.

By means of the Lorentz Transformation, Einstein's Special Theory of Relativity purports invariance of the standard wave equation. Counter-examples, satisfying the Lorentz Transformation, and hence Lorentz Invariance, prove that the Lorentz Transformation does not in fact produce invariance of the standard wave equation. Systems of clock-synchronis...

Einstein's Special Theory of Relativity requires systems of clock-synchronised stationary observers and the Lorentz Transformation. Without both, the Theory of Relativity fails. A system of clock-synchronised stationary observers is proven inconsistent with the Lorentz Transformation, because it is Galilean. The Special Theory of Relativity insists...

Time dilation is a principal feature of the Special Theory of Relativity. It is purported to be independent of position, being a function only of uniform relative velocity, via the Lorentz Transformation. However, it is not possible for a 'clock-synchronised stationary system' of observers K to assign a definite time to any 'event' relative to a 'm...

Length contraction is a principal feature of the Special Theory of Relativity. It is purported to be independent of position, being a function only of uniform relative velocity, via systems of clock-synchronised stationary observers and the Lorentz Transformation. However, a system of stationary observers reports not length contraction but length e...

Physicists since Einstein have assumed that the Galilean system of clock-synchronised stationary observers is consistent with the Special Theory of Relativity. More specifically , they have always assumed that the Galilean system of clock-synchronised stationary observers, that obeys the Galilean transformation equations, is consistent with the non...

Einstein's Special Theory of Relativity employs both clock synchronisation and the Lorentz Transformation. Without both the Theory of Relativity fails. Clock synchronisation is proven inconsistent with the Lorentz Transformation. The Theory of Relativity is therefore invalid due to an intrinsic logical contradiction.

The authors in this article co-found the Catt Anomaly with the Catt Question. Although until 2001, the Catt Question was called the Catt Anomaly, it was always a question about a transverse electromagnetic (TEM) wave on a transmission line. The Catt Anomaly concerns the refusal of named academic experts in classical electromagnetic theory who have...

The real world in which we dwell is characterised by four dimensions: length, breadth, height, and time. If the value of length is denoted by x, breadth by y, height by z and time by t, any time and place can be denoted by the coordinates (t, x, y, z), where the x-axis, the y-axis and the z-axis are all perpendicular to one another (Cartesian coord...

On Tuesday the 6th of December 2016, professor David Reitze, the Director of LIGO, delivered a 'keynote' conference lecture to high school science teachers at the University of Queensland. He reiterated claims that the LIGO-Vigro Collaboration detected gravitational waves produced by two merging black holes some 1.3 billion light years from Earth....

On the evening of the 29th of November 2016, Professor Manfred Lindner from the Max Planck Institute for Nuclear Physics, gave a public lecture at the University of Sydney, on dark matter and cosmology, and the Xenon1T project searching for dark matter particles by means of neutrino collisions and recoils in a 1 tonne vat of liquid xenon. At the co...

Saadeh et al recently reported in Phys. Rev. Lett. [1] that " anisotropic expansion of the Universe is strongly disfavoured , with odds of 121,000:1 against " , using CMB temperature and polarisation data from the WMAP and Planck satellites. However, it is impossible to determine anything about expansion of the Universe from the WMAP and Planck dat...

It has been reported by Huseman et al� that the active galactic nucleus of Mrk 1018 has likely changed optical type due to the effects of a supermassive black hole (SMBH) of the Schwarzschild type, or a binary system consisting of two such black holes. It is impossible for any type or form of black hole to be involved with Mrk 1018 because the math...

The LIGO Scientific Collaboration and Virgo Collaboration have announced [1] that on the 14th of September 2015, at 09:50:45 UTC, they detected a transient Einstein gravitational wave, designated GW150914, produced by two merging black holes forming a single black hole. Not so long ago similar media excitement surrounded the announcement by the BIC...

A number of methods have been employed by cosmologists to effect what they call an 'extension' of their 'Schwarzschild solution', to remove the singularity at their 'Schwarzschild radius' r s = 2Gm/c^2; the latter they maintain is the radius of the 'event horizon' of a black hole. They call the singularity at the Schwarzschild radius a coordinate s...

Over a number of years there have been some attempts to answer the Catt Question within the context of classical electromagnetic theory. None of the authors of these attempts agree on the answer to the Catt Question, even though they all invoke the very same theory. An attempt at answering the Catt Question appeared in the journal Physics Education...

The LIGO Scientific Collaboration and the Virgo Collaboration have announced that on 24 September 2015, LIGO detected an Einstein gravitational wave directly for the first time, with the first observation of a binary black hole merger. The announcement was made with much media attention. Not so long ago similar media excitement surrounded the annou...

Cosmologists always claim that their black holes, mathematical fabrications entire as they are, have a finite mass. This mass, they say, is concentrated at their ‘singularity’, where volume is zero, density is infinite, and their spacetime infinitely curved. Their singularity they say is not a mathematical artifice, not a limiting fiction, but a re...

Cosmologists always claim that their black holes, mathematical fabrications entire, have an escape velocity. They even have an equation for it and by using this equation they assert that the ‘escape velocity’ at their black hole ‘event horizon’ is the speed of light. This event horizon, they say, is at the ‘Schwarzschild radius’ of their black hole...

Cosmologists claim that they have found black holes all over the Cosmos. The black hole is however entirely a product of mathematics. The simplest case is the ‘Schwarzschild’ black hole, from the solution to Einstein’s field equations in the absence of matter, for a static, uncharged, non-rotating mass. “In the absence of matter” involves linguisti...

Australian National University astronomer Professor Brian Schmidt is a Nobel Laureate for physics. On Monday the 15th of September 2014 he appeared on the ABC national Australian television programme Q&A. His response to a question put to him by an eleven year old boy in the audience is a typical example of why it is very unwise to passively accept...

People so often place their trust in the word of an Authority that they don’t carefully think about what they have been told. Consequently, that when upon a little reflection is recognised as utter fantasy, is passively accepted as true on the word of an Authority. Perhaps physics is the most pitiful example of the word of dogmatic Authority carryi...

Various line-elements purporting different types of black hole universes have been advanced by cosmologists but a means by which the required infinite set of equivalent metrics can be generated has evaded them. Without such a means the theory of black holes is not only incomplete but also ill-posed. Notwithstanding, the mathematical form by which t...

I extend my thanks to Professor Gerardus ‘t Hooft, Nobel Laureate in Physics, for making more widely known my work on black hole theory, big bang cosmology, and Einstein’s General Theory of Relativity, by means of his personal website, and for providing me thereby with the opportunity to address the subject matter - supported by extensive reference...

Various line-elements purporting different types of black hole universes have been advanced by cosmologists but a means by which the required infinite set of equivalent metrics can be generated has evaded them. Without such a means the theory of black holes is not only incomplete but also ill-posed. Notwithstanding, the mathematical form by which t...

Affirming Kirchhoff’s Law of thermal emission, Max Planck conferred upon his own equation and its constants, h and k, universal significance. All arbitrary cavities were said to behave as blackbodies. They were thought to contain black, or normal radiation, which depended only upon temperature and frequency of observation, irrespective of the natur...

This article is the transcript of the audio-visual presentation titled ‘Wormholes: Science Fiction or Pure Fantasy?’ [7] prior to Hollywood’s release of the movie ‘Interstellar’, the plot of which involves astronauts travelling through a wormhole to save the Human Race. It is explained in simply terms why the wormhole has no relation to reality, ju...

Professor Gerardus ‘t Hooft, Nobel Laureate in Physics, Editor-in-Chief of the journal Foundations of Physics, has again brought attention to my work on black hole theory, big bang cosmology, and General Relativity, by means of his personal website, providing me thereby with the opportunity to address his most recent comments, particularly on black...

Although no theory is complete in that it is perfect and never needing update or modification with the discovery of new experimental facts, that is very different to a theory being logically inconsistent and also different to a theory being in conflict with a fundamental principle in physics that has been established by a vast array of experiments....

The black hole is allegedly predicted by Einstein’s General Theory of Relativity. However, by comparison of the Einstein field equations for Schwarzschild spacetime and de Sitter spacetime it is plainly evident that matter is allegedly present and absent by the very same mathematical constraint: Tμν = 0. Since this is impossible, and since de Sitte...

Whenever 1 you hear cosmologists talk of a black hole they never tell you what type of black hole they allege in what type of big bang universe they allege. It is always reported something like this: there is a black hole here or there and the Universe is expanding. More often than not the black hole is mentioned without any reference to a big bang...

This is the transcript of an interview [1] in which it is explained that the BICEP2 telescope located at the South Pole did not detect anything other than galactic noise. Despite reports with great fanfare, BICEP2 did not detect the signatures of Einstein gravitational waves or an inflationary epoch in some big bang expanding universe. The reports...

In a paper dated the 22nd of January 2014, bearing the title ‘Information Preservation and Weather Forecasting for Black Holes’, Stephen Hawking has not claimed that black holes don’t exist. He has proposed that the event horizons of alleged black holes do not exist and that only apparent horizons form when gravitational collapse of a body such as...

Did the COBE, WMAP and Planck satellites really measure the temperature of the Universe? Despite all claims to have done so, the temperature of the Universe has not been determined by any of these satellites. There is no monopole signal at the Second Lagrange Point (L2).

In their paper titled The Schwarzschild metric: It’s the coordinates, stupid! the Authors (Fromholz, Poisson, Will, 2013) consider the so-called ‘Schwarzschild solution’ for “a vacuum, static spherical spacetime” and attempt to determine a general means by which equivalent solutions can be generated. They have however, failed to obtain this means,...

It is shown in this paper that the Big Bang Cosmology has its basis in theology, not in science, that it pertains to a Universe entirely filled by a single spherically symmetric continuous indivisible homogeneous body and therefore models nothing, that it violates the physical principles of General Relativity, that it violates the conservation of e...

All alleged black hole solutions pertain to a universe that is spatially infinite, is eternal, contains only one mass, is not expanding, and is asymptotically flat or asymptotically curved. But the alleged big bang cosmology pertains to a universe that is spatially finite (one case) or spatially infinite (two different cases), is of finite age, con...

The General Theory of Relativity is notoriously known for its complicated mathematics. This has been a great impediment to many who wish to understand such things as black hole theory and big bang cosmology. However, all the salient facts can be easily understood without any recourse to confusing mathematics. With these facts clearly explained in s...

Hawking and Penrose proposed “A new theorem on spacetime singularities … which largely incorporates and generalizes the previously known results” which they claimed “implies that space-time singularities are to be expected if either the universe is spatially closed or there is an ‘object’ undergoing relativistic gravitational collapse (existence of...

The eight Vigier Symposium held at a joint meeting with the British Computer Society - Cybernetics Machine Group (BCS-V8) at its national headquarters in Covent Garden, London, was very succesfull with about 50 delegates from dozen of countries. As the 52 chapters will reflect this symposium was a delightifull and erudite cornucopia of ideas. The...

This paper proves in a simple way, with minimal mathematics, that there is no black hole or close black hole binary system in Nova Scorpii, contrary to the published claims of Schmidt et al. (2002). It also consequently proves that the concept of the black hole violates the physical principles of General Relativity and is therefore invalid.

COBE (The Cosmic Background Explorer or Explorer 66), a satellite dedicated to cosmology and WMAP (The Wilkinson Microwave Anisotropy Probe or Explorer 80) is a spacecraft which measures Cosmic Microwave Background Radiation have been considered by Pierre-Marie Robitaille, a Professor of Radiology at Ohio State University, as a failure. She assesse...

The Kruskal-Szekeres "coordinates: are said to "extend" the so-called "Schwarzschild solution", to remove an alleged "coordinate singularity" at the event horizon of a black hole at $r = 2m$, leaving an infinitely dense point-mass singularity at "the origin" $r = 0$. However, the assumption that the point at the centre of spherical symmetry of the...

According to Einstein his 'Principle of Equivalence' and his laws of Special Relativity must manifest in his gravitational field. It is shown herein that Ric = Rµ� = 0 violates Einstein's 'Principle of Equivalence'. This has major implications for gravitational waves generally because it results in the total energy of Einstein's gravitational field...

Careful reading of the reported geometry of Einstein's gravitational field re-veals that the physicists have committed fatal errors in the elementary differ-ential geometry of a pseudo-Riemannian metric manifold. These elementary errors in mathematics invalidate much of the reported physics of Einstein's gravitational field. The consequences for as...

It is demonstrated herein that:- 1.The Theory of Relativity forbids the existence of point-mass singularities be- cause they imply infinite energies (or equivalently, that a material body can acquire the speed of light in vacuo); 2.Ric=Rµ =0 violates Einstein's 'Principle of Equivalence' and so does not de- scribe Einstein's gravitational field; 3....

There are a number of conceptual anomalies occurring in the Standard exposition of Einstein's Theory of Relativity. These anomalies relate to issues in both mathematics and in physics and penetrate to the very heart of Einstein's theory. This paper reveals and amplifies a few such anomalies, including the fact that Einstein's field equations for th...

Using a manifold with boundary various line-elements have been proposed as solutions to Einstein’s gravitational field. It is from such line-elements that black holes, expansion of the Universe, and big bang cosmology have been alleged. However, it has been proved that black holes, expansion of the Universe, and big bang cosmology are not consisten...

In a previous paper the writer treated of particular classes of cosmological solutions for certain Einstein spaces and claimed that no such solutions exist in relation thereto. In that paper the assumption that the proper radius is zero when the line-element is singular was generally applied. This general assumption is unjustified and must be dropp...

The usual interpretations of solutions for Einstein’s gravitational field satisfying the spherically symmetric condition contain anomalies that are not mathematically permissible. It is shown herein that the usual solutions must be modified to account for the intrinsic geometry associated with the relevant line elements.

It is alleged by the Standard Cosmological Model that Einstein's Universe is finite but unbounded. Although this is a longstanding and widespread allegation, it is nonetheless incorrect. It is also alleged by this Model that the Universe is expanding and that it began with a Big Bang. These are also longstanding and widespread claims that are demon...

It is proved herein that the metric in the so-called “isotropic coordinates” for Einstein’s gravitational field is a particular case of an infinite class of equivalent metrics. Furthermore, the usual interpretation of the coordinates is erroneous, because in the usual form given in the literature, the alleged coordinate length sqrt(dx2+dy2+dz2) is...

The Regge-Wheeler tortoise “coordinate” and the the Kruskal-Szekeres “extension” are built upon a latent set of invalid assumptions. Consequently, they have led to fallacious conclusions about Einstein’s gravitational field. The persistent unjustified claims made for the aforesaid alleged coordinates are not sustained by mathematical rigour. They m...

The alleged existence of so-called Planck particles is examined. The various methods for deriving the properties of these “particles” are examined and it is shown that their existence as genuine physical particles is based on a number of conceptual flaws which serve to render the concept invalid.

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...

It is generally alleged that Einstein’s theory leads to a finite but unbounded universe. This allegation stems from an incorrect analysis of the metric for the point-mass when λ 0. The standard analysis has incorrectly assumed that the variable r denotes a radius in the gravitational field. Since r is in fact nothing more than a real-valued paramet...

Relativistic motion in the gravitational field of a massive body is governed by the external metric of a spherically symmetric extended object. Consequently, any solution for the point-mass is inadequate for the treatment of such motions since it pertains to a fictitious object. I therefore develop herein the physics of the standard tests of Genera...

The black hole, which arises solely from an incorrect analysis of the Hilbert solution, is based upon a misunderstanding of the significance of the coordinate radius r. This quantity is neither a coordinate nor a radius in the gravitational field and cannot of itself be used directly to determine features of the field from its metric. The appropria...

I derive herein a general form of Kepler's 3rd Law for the general solution to Einstein's vacuum field. I also obtain stable orbits for photons in all the configurations of the point-mass. Contrary to the accepted theory, Kepler's 3rd Law is modified by General Relativity and leads to a finite angular velocity as the proper radius of the orbit goes...

The vacuum field of the point-mass is an unrealistic idealization which does not occur in Nature - Nature does not make material points. A more realistic model must therefore encompass the extended nature of a real object. This problem has also been solved for a particular case by K. Schwarzschild in his neglected paper on the gravitational field o...

We report on the current status of the University of New South Wales Extrasolar Planet Search project, giving details of the methods we use to obtain millimagnitude precision photometry using the 0.5-m Automated Patrol Telescope. We use a novel observing technique to optimally broaden the point spread function and thus largely eliminate photometric...

The general solution to Einstein’s vacuum field equations for the point-mass in all its configurations must be determined in such a way as to provide a means by which an infinite sequence of particular solutions can be readily constructed. It is from such a solution that the underlying geometry of Einstein’s universe can be rightly explored. I repo...

In a previous paper I derived the general solution for the simple point-mass in a true Schwarzschild space. I extend that solution to the point-charge, the rotating point-mass, and the rotating point-charge, culminating in a single expression for the general solution for the point-mass in all its configurations when Λ = 0. The general exact solutio...

We report on the current status of the University of New South Wales Extrasolar Planet Search project, giving details of the methods we use to obtain millimagnitude precision photometry using the 0.5m Automated Patrol Telescope. We use a novel observing technique to optimally broaden the PSF and thus largely eliminate photometric noise due to intra...

The relativists have not understood the geometry of Einstein's gravitational field. They have failed to realise that the geometrical structure of spacetime manifests in the geometrical relations between the components of the metric tensor. Consequently, they have foisted upon spacetime quantities and geomet-rical relations which do not belong to it...

The so-called 'Schwarzschild solution' is not Schwarzschild's solution, but a corruption, due to David Hilbert (December 1916), of the Schwarzschild/Droste solution, wherein m is allegedly the mass of the source of an associated gravitational field and the quantity r is said to be able to go down to zero (although no proof of this claim has ever be...

Some claims of standard model cosmology are tested with the inhomogeneous field equation of ECE field theory. The only rigorously correct line elements available at present are those given by Crothers, because they are the only line elements that are geometrically correct as well as being exact solutions of the Einstein Hilbert (EH) field equation....

It is proved herein that the quantity 'r' appearing in the so-called "Schwarzschild so- lution" is neither a distance nor a geodesic radius but is in fact the radius of Gaussian curvature. The radius of Gaussian curvature does not determine the geodesic radial distance (the proper radius) from the arbitrary point at the centre of spherical sym- met...

The usual interpretations of solutions for the gravitational field in a spherically symmetric Type I Einstein space contain mathematical anomalies. It is shown herein that the usual solutions must be modified to account for the intrinsic geometry associated with the rele- vant line elements, by which the geometrical relations between the components...

The Coulomb and Ampere Maxwell laws are calculated exactly from Einstein Cartan Evans (ECE) unified field theory. The result are given for several stationary and dynamical line elements and metrics of the Einstein Hilbert field equation, and show that in general there are relativistic corrections of the same order as those responsible for the defle...

It is demonstrated herein that:- 1. The quantity ‘r’ appearing in the so-called “Schwarzschild solution” is neither a distance nor a geodesic radius in the manifold but is in fact the inverse square root of the Gaussian curvature of the spatial section and does not generally determine the geodesic radial distance (the proper radius) from the arbitr...

The claims to existence of black holes in nature are refuted in several ways, and several fundamental errors of the theory are pointed out. The most basic error is that the Einstein field equation violates the Cartan/Evans dual iden-tity of geometry, as shown in previous papers of this series. Several com-monly used metrics of black hole theory are...

The usual interpretations of solutions for Einstein's gravitational field satisfy-ing the static vacuum conditions contain anomalies that are not mathemati-cally permissible. It is shown herein that the usual solutions must be modified to account for the intrinsic geometry associated with the relevant line-elements.

A recent Letter to the Editor (Sharples J. J., Coordinate transformations and metric ex-tension: a rebuttal to the relativistic claims of Stephen J. Crothers, Progress in Physics, v.1, 2010) has analysed a number of my publications in Progress in Physics. There are serious problems with this treatment which should be brought to the attention of the...