Schwarzschild solution and its implications for gravitational waves

Am 12. März 2009 erhielt ich von Stephen Crothers, Queensland Australien, folgende zwei Dateien (conference papers) mit E-Mail zugesandt. Diese betreffen einen Vortrag von Stephen Crothers bei der Deutschen Physikalischen Gesellschaft, München, März 2009, Fachverband Gravitation und Relativitätstheorie. Diese beiden Dateien habe ich inzwischen auf meine Server gegen habe, siehe:  und  

Nachstehend bringe ich Auszüge hieraus. 


Conference of the German Physical Society, Munich, March 9-13, 2009.
Verhandlungen der Deutsche Physikalische Gesellschaft
Munich 2009: Fachverband Gravitation und Relativitätstheorie 

The Schwarzschild solution and its implications for gravitational waves
Stephen J. Crothers
Queensland, Australia, 
2 November 2008 

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 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 a 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, in a very real sense, removal of the wrong singularity, very simply demonstrated herein. This has major implications for the localisation of gravitational energy i.e. gravitational waves. 

[ . . . . . . . . ]

X. Conclusions

„Schwarzschild’s solution“ is not Schwarzschild’s solution. Schwarzschild’s actual solution does not predict black holes. The quantity ‚r‘ appearing in the so-called „Schwarzschild solution“ is not a distance of any kind in the associated manifold – it is the inverse square root of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section. This simple fact completely subverts all claims for black holes.

The generalisation of Minkowski spacetime to Schwarzschild spacetime, via Ric = 0, is not a generalisation of Special Relativity. Neither Einstein’s ‚Principle of Equivalence‘ nor his laws of Special Relativity can manifest in a spacetime that by construction contains no matter. Therefore, Ric = 0, a spacetime that by construction contains no matter, violates Einstein’s ‚Principle of Equivalence‘. Similarly, Ric = _g?_ , a spacetime that by construction contains no matter, also violates Einstein’s ‚Principle of Equivalence‘ and his laws of Special Relativity, and so cannot describe a gravitational field.

The Riemann tensor scalar curvature invariant (the Kretschmann scalar) is not an independent curvature invariant – it is a function of the Gaussian curvature of the spherically symmetric geodesic surface in the spatial section. Gaussian curvature is an intrinsic geometric property of a surface, determined from the components and their derivatives of the metric tensor of the First Fundamental Form for a surface.

Despite claims for discovery of black holes, nobody has ever found a black hole; no infinitely dense point-mass singularity and no event horizon have ever been found. There is no physical evidence for the existence of infinitely dense point-masses. It takes an infinite amount of observer time to verify the presence of an event horizon, but nobody has been and nobody will be around for an infinite amount of time. No observer, no observing instruments, no photons, no matter can be present in a spacetime that by construction contains no matter. The black hole is fictitious and so there are no black hole generated gravitational waves. The international search for black holes and their gravitational waves is ill-fated.

The Michell-Laplace dark body is not a black hole. Newton’s theory of gravitation does not predict black holes. General Relativity does not predict black holes. Black holes were spawned by (incorrect) theory, not by observation [2, 3, 4, 7, 28]. The search for black holes is destined to find none.

Curved spacetimes without material cause violate the physical principles of General Relativity. There is no experimental evidence supporting the notion of gravitational fields generated without material cause.

No celestial body has ever been observed to undergo irresistible gravitational collapse. There is no laboratory evidence for irresistible gravitational collapse. Infinitely dense point-mass singularities howsoever formed cannot be reconciled with Special Relativity, i.e. they violate Special Relativity, and therefore violate General Relativity.

General Relativity cannot account for the simple experimental fact that two fixed bodies will approach one another upon release. There are no known solutions to Einstein’s field equations for two or more masses and there is no existence theorem by which it can even be asserted that his field equations contain latent solutions for such configurations of matter. All claims for black hole interactions are invalid.

Einstein’s gravitational waves are fictitious; Einstein’s gravitational energy cannot be localised; so the international search for Einstein’s gravitational waves is destined to detect nothing. No gravitational waves have been detected. Einstein’s pseudo-tensor is meaningless and linearisation of Einstein’s field equations inadmissible. And the Lense-Thirring effect was not detected by the Gravity Probe B.

Einstein’s field equations violate the experimentally well-established usual conservation of energy and momentum, and therefore violate the experimental evidence. 


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