Is the Schwarzschild Black Hole Spurious?

2008

The so-called 'Schwarzschild solution' is not Schwarzschild's solution, but a corruption of the Schwarzschild/Droste solution due to David Hilbert (December 1916), wherein m is allegedly the mass of the source of the alleged associated 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 alleged 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 usual metric has never been rightly identified by the physicists, who effectively treat it as a radial distance from the alleged 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 in the procedures applied to the associated metric by which the black hole has been generated. 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 Schwarzschild spacetime and so does not denote radial distance in the Schwarzschild 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 actually a removal of the wrong singularity, very simply demonstrated herein.

Arxiv preprint gr-qc/0001007, 2000

2005

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 Λ = 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.

A review of results about this paradigmatic solution 1 to the field equations of Einstein's theory of general relativity is proposed. Firstly, an introductory note of historical character explains the difference between the original Schwarzschild's solution and the "Schwarzschild solution" of all the books and the research papers, that is due essentially to Hilbert, as well as the origin of the misnomer. The viability of Hilbert's solution as a model for the spherically symmetric field of a "Massenpunkt" is then scrutinised. It is proved that Hilbert's solution contains two main defects. In a fundamental paper written in 1950, J.L. Synge set two postulates that the geodesic paths of a given metric must satisfy in order to comply

Communications in Physics

In this paper, based on the vector model for gravitational field we deduce an equation to determinate the metric of space-time. This equation is similar to equation of Einstein. The metric of space-time outside a static spherically symmetric body is also determined. It gives a small supplementation to the Schwarzschild metric in General theory of relativity but the singularity does not exist. Especially, this model predicts the existence of a new universal body after a black hole.

A new point of view is presented for which the Schwarzschild singularity becomes a real point singularity on which the sources of Schwarzschild's exterior solution are localized.

2008

The modern notion of a black hole singularity is considered with reference to the Schwarzschild solution to Einstein's field equations of general relativity. A brief derivation of both the original and the modern line elements is given. The argument is put forward that the singularity occurring within the Schwarzschild line element that has been associated with the radius of the black hole event horizon is, in fact, merely a mathematical occurrence and does not exist physically. The real aim here, however, is to attempt to open up the whole problem, draw some conclusions, but finally to urge everyone to consider the points raised with no preconceived opinions and then come to their own final conclusion.

Advances in High Energy Physics, 2014

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path ...