Alpha Institute for Advanced Studies (AIAS)

Criticisms of Vacuum Big Bang (Stephen Crothers)

I would like to pursue further the issues addressed in my previous email.

In the case of the solutions for Ric = 0 it is plain that the black hole is a phantasm: on four grounds, each of which is of itself sufficient to prove the falsity of the notion.

1. Since Ric = 0 does not describe Einstein's gravitational field there is no black hole (Schwarzschild or Kerr);
2. Since there is no "removable" singularity due to a "coordinate pathology" in the so-called "Schwarzschild solution" there is no black hole;
3. The singularity of all black holes is allegedly an infinitely dense point-mass. However, Special Relativity forbids infinite densities because infinite density implies infinite energy (or equivalently that a material body can acquire the speed of light in vacuo). General Relativity cannot violate Special Relativity, and so it too must forbid infinite densities, and so there are no black holes;
4. It takes an infinite amount of observer time for the presence of an event horizon to be identified by that observer, but no observer has been or will be around for an infinite amount of time to verify the presence an event horizon (but an observer must surely be composed of matter, contrary to Ric = 0 as well).

Assuming for the sake of argument that the Schwarzschild (and Kerr) black hole is consistent with General Relativity, it is clear that the Universe can consist of only that black hole and nothing else, since Ric = 0. Therefore there is nothing for the black hole to act upon (and so there is also no meaning to the 'angular momentum' of the Kerr black hole). Furthermore, it is clear that the notion of two or more such black holes interacting is nonsense since each black hole is derived from Ric = 0 and so one cannot merely insert into the empty space-time of a given black hole a second black hole (also obtained from Ric = 0 separately) so that the two (or more) black holes talk to one another in a mutual space-time that for each black hole, by definition, contains no matter! One cannot by an analogy with Newton's theory merely insert black holes at whim into the empty space-time (Ric = 0) of a given black hole and then also claim that they can be binary, merge or collide. One needs a non-zero energy-momentum tensor describing the configuration of two (or more) interacting masses and then a solution to Einstein's field equations for it to make any sense of gravitational coupling. That has never been done and there is no existence theorem by which it can even be asserted that Einstein's field equations contain latent solutions for such configurations of matter. To date, Einstein's theory has not been able to account for the simple experimental fact that two fixed ponderable bodies will approach one another upon release.

Since Ric = 0 does not describe Einstein's gravitational field, his field equations become:

Gμν/κ + Tμν = 0

where the Gμν/κ are the components of a gravitational energy tensor. Thus the total energy is always zero; Einstein's tensor and the energy-momentum tensor must vanish identically; there is no possibility of the localisation of gravitational energy (i.e. no Einstein gravitational waves). Einstein's conceptions of the localisation and conservation of gravitational energy are false. Moreover, Einstein's theory is thus in conflict with the long experimentally established principle of the conservation of energy and momentum. In an attempt to avoid this outcome Einstein invented his pseudo-tensor for gravitational energy. However, the foregoing cannot be circumvented. This is reaffirmed by the fact that Einstein's pseudo-tensor is a meaningless concoction of mathematical symbols – it implies the existence of a 1st-order intrinsic differential invariant that depends only upon the components of the metric tensor and its first derivatives (to see this contract his pseudo-tensor and apply Euler's theorem). But the mathematicians Ricci and Levi-Civita proved in 1900 that such invariants do not exist! Thus Einstein's pseudo-tensor and everything based upon it are nonsense. In addition, the Standard Model linearization of the field equations is actually impossible because linearization implies the existence of a tensor that, except for the trivial case of being precisely zero, does not otherwise exist, as proved by H. Weyl in 1944.

Big bang and the FRW line-element are invalid for the very same geometrical reason of Gaussian curvature and for the prohibition of infinite densities by the Theory of Relativity, just as in the case of the black hole.

Steve Crothers.