Gerhard W. Bruhn, Darmstadt University of Technology

9 Oct 2008

Subject: Major Errors in Carroll Chapter Seven Date: Thu, 9 Oct 2008 05:35:24 EDT

Dear Prof. Carroll,

I went through your chapters one to three of your notes and these are correct, I have gone through everything and also expanded greatly on the proofs. I found Cartan geometry to be very useful, and the tetrad postulate is correct. However, we have used computer algebra to show beyond doubt that black hole and big bang theories are incorrect (see papers 93 onwards on _www.aias.us_ (http://www.aias.us) ). Thsi mesn that there is no dark matter, and no Hawking radiation and so on. The fundamental problem is that neglect of torsion leads to a violation of the dual Bianchi identity (proven in many ways in the ECE papers on _www.aias.us_ (http://www.aias.us) ). This means that the Einstein field equation is geometrically incorrect, and all solutions thereof are incorrect also. We have checked this very carefully in a whole series of papers. You recognize the role of torsion in your chapter three, one of the very few to do so. In the ECE engineering model on _www.aias.us_ (http://www.aias.us) we have developed new equations of dynamics based on the Bianchi identity, and torsion plays a central role. Unfortunately therefore your chapters 4 to 8 contain many errors which have been handed down from about 1900, when Ricci and Levi Civita first introduced the symmetric connection. In papers 93, 95 and 117 on _www.aias.us_ (http://www.aias.us) computer algebra is used to show in great detail how this leads to a violation of the correct Bianchi identity of Cartan, (circa 1922 ff.). It is particularly important to refute big bang and black hole theory, because a lot of nonsense about it proliferates on TV and so on. In paper 120 we will severely criticise black hole theory. There are many errors in this chapter. For example.

1) In eq. (7.5) the generally symmetric metric leads in general to a violation of the dual identity.

However, that ''dual identity'' does not hold in general as proven by several counter-examples given by the Evans-crew itself. See Evans' Duality Experiments.

2) Similarly the generally symmetric metric (7.13) leads to a violation of the dual identity.

No miracle, since the ''dual identity'' is invalid in general.

3) In eq. (7.26), r should be r - r0 as pointed out by Schwarzschild, Dunning-Davies and Crothers independently. There is no black hole singularity. Additionally this is a metric derived from a null Ricci tensor, so there is no canonical energy momentum density present and no mass. This metric and all vacuum metrics are physically meaningless, they deal with a universe with nothing at all in it.

r0 is not defined by Carroll. If any r0 ≠ 0 should be meant (Crothers) then this remark is wrong: The preceeding de. (7.24) does not admit any r0 ≠ 0.

4) In eq. (7.30) there is a false singularity, r should be r - r0.

Nonsense! See the preceeding comment.

5) The condition r c squared exp (2 alpha) = 1 - 2GM / (r c squared) must be positive or zero. This was pointed out recently by Crothers.

What a deep insight! With respect to his Eq.(7.29) on the following pages Carroll considers just this case 2GM < r (setting c=1).

6) The Eddington Finkelstein transformation merely transforms one version of a null Ricci metric to another. There is no physics here, just a vacuum.

No physics just for people who cannot follow such a simple consideration.

7) We have shown by computer algebra that the Kruskal transformation is incorrect, it produces a non-null Einstein tensor from an initially null Einstein tensor, and violates the dual identity.

No miracle for the dual identity since being invalid in general. The Einstein tensor of the
Kruskal metric is the coordinate transformed Einstein tensor of the Schwarzschild metric
connected by a *homogeneous bilinear* transform due to the rules of tensor calculus.
Thus a correct calculation of the coordinate transform
must give vanishing Einstein tensor of the Kruskal metric as well. The failing of the computer algebra
is possibly due to ~~an input error~~
incomplete computer calculations
of people who are untrained in math and do not understand the response of their
computers.

8)The null version of the Kruskal transformation is also incorrect.

Which ''null version''?

9) There can be no Hawking radiation, we have tested by computer that this theory is also incorrect because of neglect of torsion. There are no black holes in nature, no big bang and no dark matter. A great amount of pseudo-science is all that these ideas amount to.

Hawking radiation is not considered in Chap.7.

10) We tested by computer algebra that the Reissner Nordstrom. Kerr, Kerr Newman and FLRW metrics also violate the dual identity due to neglect of torsion.

The ''dual identity'' does not hold! See Evans' Duality Experiments.

Therefore the whole of twentieth century gravitational theory is obsolete. This has been pointed out to Hawking and Rees. I believe that Penrose has retired. All of this is well known by now and well accepted, and we are proceeding with our own equations of dynamics and our own methods of publishing and education. Twentieth century gravitational theory was just pseudo-physics, and will be increasingly rejected. The above criticisms are simple to understand and cannot be remedied without proper inclusion of torsion.

British Civil List Scientist

This last conclusion is as wrong as the preceeding ones. See the Remarks to 1).