To publish an article presenting an ether interpretation of General Relativity is far away from being easy - even if the very existence of such an interpretation would be interesting for many people, I would say, from experience, that almost no journal would even consider it for publication. To publish it, one needs some formal justification, which makes it hard to reject a publication.

So, seeing in the American Journal of Physics an article A.J.S. Hamilton, J.P. Lisle, The river model of black holes, which has proposed some nice special coordinates for black hole solutions, and described them as a sort of "river model" for black holes, I have seen a possibility to present the Lorentz ether interpretation as a much better "river model" in comparison with what has been proposed there. Critizing an already published paper, and proposing an improvement, which does not have the mentioned problems - this is clearly a good justification for the publication of an article.

But it doesn't help always. Even if any honorable journal would, I think, publish a criticism of a published paper, which even suggests an improvement, if only the criticism itself has been accepted as valid by the authors of the criticized article, the situation is different if the improvement suggested is an ether interpretation of GR. So, the submission has been rejected by AJP.

Here is the article itself: About "river models" for general relativity.

Here is the review by one of the authors of the criticized article, A.J.S. Hamilton:

Title: About "river models" for general relativity

Author: I. Schmelzer

Referee: Andrew J. S. HamiltonI enjoyed reading this thought-provoking paper. In my opinion the paper deserves publication in AJP.

The paper is quite critical of our paper Hamilton & Lisle published in AJP in 2008. I accept those criticisms; that is to say, I agree that our "river model" for black holes does not generalize to all possible spacetimes in GR, and in that sense is not fundamental. However, I think that our "river model" remains the best way to teach a valid conceptual picture of black holes that students and the general public can understand. It is certainly much better than the "rubber-sheet" analogy. In my view, the most important thing to understand about black holes is the horizon (next being the singularity). Our "river model" does a great job with respect to these priorities. As this paper puts it, "these theories allow the students to develop reasonable intuitions about what happens. This is possibly even more important than teaching the mathematics of these theories itself."

The author advocates a different "river model" based on a preferred choice of coordinates. The preferred choice follows from choosing the coordinates to satisfy a wave equation, the so-called harmonic gauge condition (the choice is not unique, unless supplemented by boundary conditions). The harmonic time and space coordinates then satisfy, by construction, equations that look like fluid equations, with the fluid stress playing the role of the 6 physical gravitational degrees of freedom.

The paper makes plain the drawbacks of the proposed "river model." One of these is that harmomic coordinates blow up at the horizon rather than continuing through the horizon. This alone makes the proposed river model of little use for teaching black holes conceptually to a non-professional audience. Still, mathematics and physics students learning gr properly should find it interesting that gr can be treated in this fashion.

At the heart of this paper is the fundamental question of whether a special coordinate system can be identified. By itself gr is generally covariant and locally Lorentz invariant, and there is no preferred frame. But in the real Universe, there is a special frame in cosmology, that of the cosmic microwave background. The cmb is not Lorentz-invariant. If the standard inflationary paradigm is correct, then Lorentz symmetry must have been broken at some early time when the parts of our Universe were in causal contact. What broke that symmetry? The cmb frame holds even in parts of parts of the universe where matter has collapsed into highly nonlinear systems such as galaxies and solars systems. One can even imagine following the cmb frame inside black holes.

There is consensus in the quantum community that gr can only be an effective low energy theory. Arguably the most promising developments lately have been coming out of the AdS-CFT duality in string theory. It has been claimed that black holes in AdS-CFT are horizonless "fuzzballs," extended stringy objects in which the string size extends to the horizon http://arxiv.org/abs/1506.04342. Necessarily, the calculations that lead to fuzzballs are idealized. Fuzzball black holes absorb and emit Hawking radiation, but unlike astronomical black holes they are not constantly being bombarded by high energy (compared to Hawking) particles such as cmb photons.

This raises the question, does gr remain a good decription of spacetime even when there is no matter or radiation to probe it?

The paper states "One unfortunate result of actual teaching of relativity is the abundance of "ether cranks"." Like the poor, cranks will be with us always. I don't think it helps "experts" to censor arguments for fear of misleading cranks.

See M. Abe, S. Ichinose, and N. Nakanishi "Kerr Metric, De Donder Condition and Gravitational Energy Density" Prog. Theor. Phys. 78 (1987), 1186, for the full (complicated) expression for Kerr-Newman in harmonic coordinates.

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