Abstracts Details

Also published in *Global Journal of Science Frontier Research Physics and Space Science* **12** (4): 1-4 (June 2012). 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 proves that the concept of the black hole violates the physical principles of General Relativity and is therefore invalid.

The black hole, gravitational waves, and the Big Bang cosmology have no valid basis in science. It is demonstrated herein that Einstein's field equations violate the usual conservation of energy and momentum and are therefore in conflict with experiment on a deep level, so that General Relativity is invalid. This fact alone proves the invalidity of the black hole, gravitational waves, the Big Bang cosmology and Einstein's conception of the gravitational field.

The black hole and the Big Bang cosmology have no valid basis in science. It is demonstrated herein that Einstein's field equations violate the usual conservation of energy and momentum and therefore violate the well established experimental results. This fact alone proves the invalidity of the black hole and the Big Bang cosmology. This paper is a shortened version of a more detailed analysis which can be obtained at www.sjcrothers.plasmaresources.com/BB.pdf.

It is often claimed that cosmology became a true scientific inquiry with the advent of the General Theory of Relativity. A few subsequent putative observations have been misconstrued in such a way as to support the prevailing Big Bang model by which the Universe is alleged to have burst into existence from an infinitely dense point-mass singularity. Yet it can be shown that the General Theory of Relativity and the Big Bang model are in conflict with well-established experimental facts.

Black holes are not without cosmological significance in view of the many claims routinely made for them, and so they are treated here in some detail. But the theory of black holes is riddled with contradictions and has no valid basis in observation. Nobody has ever found a black hole, even though claims for their discovery are now made on an almost daily basis. Nobody has ever found an infinitely dense point-mass singularity and nobody has ever found an event horizon, the tell-tale signatures of the black hole, and so nobody has ever found a black hole. In actuality, astrophysical scientists merely claim that there are phenomena observed about a region that they cannot see and so they illogically conclude that the unseen region must be a black hole, simply because they believe in black holes. In this way they can and do claim the presence of a black hole as they please. But that is not how science is properly done. Moreover, all black hole solutions pertain to one alleged mass in the Universe, whereas there are no known solutions to Einstein?s field equations for two or more masses, such as two black holes. In other words, the astrophysics community has no solution to Einstein?s field equations that can account for the presence of two or more bodies, yet they claim the existence of black holes in multitudes, interacting with one another and other matter.

Owing to the very serious problems with the Big Bang hypothesis and the theory of black holes, it is fair to say that neither meets the requirements of a valid physical theory. They are products of a peer review system that has gone awry, having all the characteristics of a closed academic club of mutual admiration and benefit into which new members are strictly by invitation only. The upshot of this is that the majority of the current astrophysics community is imbued with the dogmas of the academic club and the voice of dissent conveniently ignored or ridiculed, contrary to the true spirit of scientific inquiry. This method has protected funding interests but has done much harm to science.

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 ?Schwarzschild solution? is at ?the origin? r = 0 is erroneous, and so the Kruskal-

Szekeres ?extension? is invalid; demonstrated herein by simple counter-examples.

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 a gravitational field and the quantity *r* is alleged to be able to go down to zero (although no valid proof of this claim has ever been advanced), so that there are two alleged 'singularities', one at *r = 2m* and another at *r = 0*. It is routinely asserted that *r = 2m* is a 'coordinate' or 'removable' singularity which denotes the so-called 'Schwarzschild radius' (event horizon) and that the 'physical' singularity is at *r = 0*. The quantity *r* in the so-called 'Schwarzschild solution' has **never** been rightly identified by the physicists, who, although proposing many and varied concepts for what *r* therein denotes, effectively **treat it** as a radial distance from the claimed source of the gravitational field at the origin of coordinates. The consequence of this is that the intrinsic geometry of the metric manifold has been violated. It is easily proven that the said quantity *r* is in fact the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section of the 'Schwarzschild solution' and so does not in itself define any distance whatsoever in that manifold. With the correct identification of the associated Gaussian curvature it is also easily proven that there is only one singularity associated with all Schwarzschild metrics, of which there is an infinite number that are equivalent. Thus, the standard removal of the singularity at *r = 2m* is erroneous, as the alleged singularity at *r = 0* does not exist, very simply demonstrated herein. This has major implications for the localisation of gravitational energy, i.e. gravitational waves. Schwarzschild's actual solution **forbids black holes** !

It is demonstrated herein that:

- 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 centre of spherical symmetry of a 3-D spherically symmetric metric manifold.
- The Theory of Relativity forbids the existence of point-mass singularities because they imply in nite energies (or equivalently, that a material body can acquire the speed of light in vacuo).
- R
_{ic}= Ruv = 0 violates Einstein's 'Principle of Equivalence' and so does not describe Einstein's gravitational field. - Einstein's conceptions of the conservation and localisation of gravitational energy are invalid.
- The concepts of black holes and their interactions are ill-conceived.
- Expansion of the Universe and Big bang cosmology are inconsistent General Relativity.

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 the so-called static vacuum configuration, R_{uv} = 0, violates his Principle of Equivalence, and is therefore erroneous. This has a direct bearing on the usual concept of conservation of energy for the gravitational field and the conventional formulation for localisation of energy using Einstein's pseudo-tensor. Misconceptions as to the relationship between Minkowski spacetime and Special Relativity are also discussed, along with their relationships to the pseudo-Riemannian metric manifold of Einstein's gravitational field, and their fundamental geometric structures pertaining to spherical symmetry.

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 demonstrably false. The FRWmodels for an expanding, finite, unbounded Universe are inconsistent with General Relativity and are therefore invalid.

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 consistent with General Relativity. In a previous paper disproving the black hole theory, the writer made an error which, although minor and having no effect on the conclusion that black holes are inconsistent with General Relativity, is corrected herein for the record.

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 dropped. Consequently, solutions do exist in relation to the aforementioned types, and are explored herein. The concept of the Big Bang cosmology is found to be inconsistent with General Relativity.

Sepp Hasslberger blog, blog.hasslberger.com/2007/03/the_big_bang_in_controversy.html, March 14, 2007, posted October 2009.

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 ??(dx^{2} + dy^{2} + dz^{2}) is not a coordinate length. This arises from the fact that the geometrical relations between the components of the metric tensor are invariant and therefore bear the same relations in the isotropic system as those of the metric in standard Schwarzschild coordinates.

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 must therefore be discarded.

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 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. The following essay provides a brief but accurate account of events, verifiable by reference to the original papers, by which the scandalous manipulation of both scientific and public opinion is revealed.

It is generally alleged that Einstein?fs theory leads to a finite but unbounded universe. This allegation stems from an incorrect analysis of the metric for the point-mass when ?? <> 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 parameter for the actual radial quantities in the gravitational field, the standard interpretation is erroneous. Moreover, the true radial quantities lead inescapably to ??=0 so that, cosmologically, Einstein?fs theory predicts an infinite, static, empty universe

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 General Relativity by means of the generalised solution for the field external to a sphere of incompressible homogeneous fluid.

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 appropriate quantities on the metric for the gravitational field are the proper radius and the curvature radius, both of which are functions of *r.* The variable *r* is actually a Euclidean parameter which is mapped to non-Euclidean quantities describing the gravitational field, namely, the proper radius and the curvature radius.

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 down to zero, without the formation of a black hole. Finally, I generalise the expression for the potential function of the general solution for the point-mass in the weak field.

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 of a sphere of incompressible fluid. I revive Schwarzschild?s solution and generalise it. The black hole is necessarily precluded. A body cannot undergo gravitational collapse to a material point.

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 report here on the determination of the general solution and its consequences for the theoretical basis of relativistic degeneracy, i. e. gravitational collapse and the black hole.

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 pointmass, and the rotating point-charge, culminating in a single expression for the general solution for the point-mass in all its configurations when ? = 0. The general exact solution is proved regular everywhere except at the arbitrary location of the source of the gravitational field. In no case does the black hole manifest. The conventional solutions giving rise to various black holes are shown to be inconsistent with General Relativity.