From: GWB

To: Dmitri Rabounski

Cc: Larissa Borissova

Sent: Tuesday, 6 May, 2008 5:48:42 AM

Subject: Open letter to you, editor-in-chief of PP

Dear Dr. Rabounski,

let me inform you that I have posted an "Open Letter" to you
concerning the black hole publications in PP. Please, find
the open letter at

http://www2.mathematik.tu-darmstadt.de/~bruhn/toRabounski030508.html

It is a response to emails I received during the last weeks from you and your co-editor Dr. L. Borissova.

Your scientific remarks are welcome.

Best regards

Gerhard W. Bruhn

Dmitri Rabounski wrote:
*
*

* Dear Prof Bruhn,
*

* Thank you for your effort to pay attention to Crothers' papers on the black hole problem. I looked through your web-page you referred for. I however
found, in brief, that you are still talking about different things than we are. We told you about the representation with the observable quantities which
give really observed effect, while you told about the coordinate quantities. Of course, no one discuss that the black hole solution can be obtained with
the coordinate quantities where the spatial section is free of fixation so that the space-time is not split into spatial sections pierced by time lines, but is still
remaining a whole continuum. But all that had been said by me (and also by Larissa), fighting for Crothers' papers, is related to physical observable
quantities which give really observable effect and no the black hole solution on Schwarzschild's metric.
*

* You're waiting for my discussing incorrecteness of Crothers' claim or that by yours, but these are different approaches which give different results. I only
try to give you understanding that there are two different mathematical approaches to the same problem. The metrics g and h are the same; the are
different in the properties, and so on in the sequel. Meanwhile, Crothers' approach can be bound meeting close to observations, because the based on
observable quantities, in contrast to the coordinate representation used before.
*

* Thank you for your attention,
*

* Dmitri
*

From: GWB

To: Dmitri Rabounski

Sent: Friday, 9 May, 2008 5:34:07 AM

Subject: Re: Open letter to you, editor-in-chief of PP

Dear Dr. Rabounski,

you wrote as essential in you last email:
*''**. . . these are different approaches which give different results. I only try to give you understanding that there are two different mathematical
approaches to the same problem. ...
''*

**This statement of yours is incorrect.**
The advantage of mathematical methods is just that one can check the correctness of
considerations by using different mathematical approaches.

If there are two authors which obtain contradicting results from approaching the same problem by two different mathematical methods then at least one of them is in error.

So who is in error in our case???

The problem is to describe the spacetime manifold that is given by the Schwarzschild metric.

(i) Standard methods of the theory of manifolds yield that the Schwarzschild metric has two disjoint validity regions S' and S'', while from your side
the existence of one of both, namely S'' (0 < r < r_{s}), is repeatedly denied.

(ii) Standard methods of the theory of manifolds, namely the transformation of the Schwarzschild coordinates t,r to Painlevé-Gullstrand coordinates T,r yield that die validity regions S' and S'' are belonging to the same manifold S.

(iii) Standard methods of the theory of manifolds, namely the discussion of the spacetime manisfold S by means of the Painlevé-Gullstrand coordinates, yield the existence of Gravitation collapse which is denied by your side.

So please take note of the fact that there are essential contradictions of your claims to the results of standard methods of the theory of manifolds.

Since the means of getting the results of the theory of manifolds by transforming Schwarzschild to Painlevé-Gullstrand coordinates are completely elementary you are challenged now to explain what is wrong in the Standard methods.

Conversely I have repeatedly pointed to the errors in the considerations on your side. Especially your argument of "observability" is strictly connected to the Schwarzschild metric in S'. You did never answer to my question what happens to your observability concept in case of say Painlevé-Gullstrand coordinates.

Kind regards

Gerhard W. Bruhn

Dmitri Rabounski schrieb:

*Dear Prof. Bruhn,
*

* Different pictures can be obtained in different coordinates. That's as a matter.
For instance, as you know all the effects of General Relativity can be
obtained in the curvilinear coordinates of a Minkowski's space, etc.
I therefore think that your words are not related to the considered problem.
*

* No doubts that the same method should give the same result with no dependance of the number of the authors, or their personality. No one disputes you
that the gravitational collapser solution can be get with the usual technics. On the other hand, another method gives another result. A condition true with
one coordinate technics can be denied if represented with another coordinate technics. That's Crothers' case. No one disputes with you about the usual
technics or results obtained with. That's normal. I therefore think that there is no reason to discuss anything.
*

* Sincerely yours,
Dmitri*

From: GWB

To: Dmitri Rabounski

Sent: Friday, 9 May, 2008 10:19:12 AM

Subject: Re: Open letter to you, editor-in-chief of PP

Dear Dr Rabounski,

you wrote:*
*

*''Different pictures can be obtained in different coordinates. That's as a matter.''*

However, **geometric properties** are those which are **invariant** under changes of
coordinates. Other ''properties'' are only reflecting the properties of the
coordinates (which are not of interest) This insight has led to the invention of tensor calculus where the transformation properties can be seen from the
indices.
*
*

*''No one disputes you that the gravitational collapser solution can be get with the usual
technics.''*

However, your author Crothers the articles by whom you have published is denying that.
*
*

*''A condition true with one coordinate technics can be denied if represented with another
coordinate technics. That's Crothers' case.''*

NO!!! See above what I have told you about geometric properties. True in ONE coordinate sytem means NOTHING. A geometric property is true under ALL coordinate systems.

Our discussion has shown that there is a lot of math you have to think over. So let's close the discussion for this time.

Thanks

Gerhard W. Bruhn

PS I shall post this discussion with you as an appendix to

http://www2.mathematik.tu-darmstadt.de/~bruhn/toRabounski030508.html

Dmitri Rabounski schrieb:
*
*

*Dear Prof Bruhn,
*

*The properties of the coordinate systems we refer for w\are those standards we observe. These are really observed quantities, in contrast to the formally
compoinents of the general covariant quantities. That's as a matter. If you are not interested in the result really expected in practice, this is only reflects your
scientific interest. (Many people are working on abstract results, nothing insulted.) Crothers used another technics that the mathematical apparatus of general
covariant quantities, so he gets another result. You try to analyse his result from the basics of general covariant technics, so you have that you get.
*

*I only try to give you this idea, as a corner-stone of your problem with Crothers' papers
on the gravitational collarger problem. Nothing more, just this one.
*

*Thank you for your responsibility,
Auf wiedersehen!
*

*Dmitri
*

From: GWB

To: Dmitri Rabounski

Sent: Friday, 9 May, 2008 12:07:11 PM

Subject: Re: Open letter to you, editor-in-chief of PP

Dear Dr. Rabounski,

here my last words to these problems of yours:

I have sketched what can be proven by the standard mathematical methods. Have a look into the text books on mathematical physics, there you'll find that all, e.g. in the Field Theory by your countrymen Landau and Lifshitz, or, available in the web, the Lecture Notes on GRT by S.M. Carroll http://xxx.lanl.gov/pdf/gr-qc/9712019

You have published articels by Crothers in your journal PP which are not compatible with the methods of mathematical physics, and therefore, as I have pointed out, wrong: That's no question of any coordinates, it's a question of using correct math. Please, compare your views with what you can find in the literature.

Best success

Gerhard W. Bruhn

Betreff:
Re: Open letter to you, editor-in-chief of PP

Datum:
Fri, 9 May 2008 09:21:58 -0700 (PDT)

Von:
Dmitri Rabounski

An:
GWB
*
*

*Dear Prof Bruhn,
*

*I pity that you dislike to study the coordinate methods in the General Theory of Relativity. These methods are described enough in Both The Classical Theory
of Fields, Fock's book, Zelmanov's book, and many others. I appreciate your belief in the general covariant methods, but the professionally relativists, who
are me Dr Borissova and many others know many other methods, the coordinate methods which are different from the general covariant methods you belief.
Those are different methods which can give different results on the same phenomenon in consider.
If you would take an interest, and many years of research in
General Relativity, you would appreciate many methods, not only the general covariant method,
I sure.
*

*Thank you very much for your attention to my letter(s).
*

*Auf wiedersehen,
Dmitri
*

To: Dr. Rabounski

Date Sa, 17 May 2008

Dear Dr. Rabounski,

I have already once replied to your opinion that
* . . . Those are different methods which can give different results on the same phenomenon in consider.
*. **This statement of yours is WRONG:**

Let me repeat: In mathematics different methods applied to the *same* math problem cannot
give *different* results.
Then there is only one conclusion: **One of the opponents does not do his math correctly.**

And let me add this: Your informations about your sources are *remarkably imprecise*.
I'm prepared to clear up any alleged contradiction if you give me *detailed* information
(author, book or paper, page and equ. no.) as is use in science. However, your citation
method is *completely insufficient*. Then we shall immediately recognize **WHO**
is going astray. As I have pointed out e.g. the inexact informations given by L. Borissova
cannot be found in Landau-Lifshitz' ''Field Theory''.

I don't know from where you take your claim that I should *dislike* coordinate methods.
**The only thing I'm really disliking in science are preconceived ideas. **
Special coordinates are advantagous for the formulation of fundamental laws. But afterwards
it is necessary to obtain a formulation that is invariant under changes of coordinates
which are required by the symmetries of the problem under consideration, e.g. in case
of spatial spherical symmetry, think of the Schwarzschild metric which can be transformed
to several other coordinate systems of important physical meaning, e.g.

− the Painlevé-Gullstrand coordinates for from infinity radially infalling (or outgoing) test-particles,

− the tortoise coordinates (t,R),
which have the property that radially infalling and outgoing light rays satisfy

t + R = constant
or
t − R = constant
respectively.

− the Eddington-Finkelstein coordinates for light radially infalling (or outgoing) from (to) infinity ,

You mentioned **V. Fock's work**. Surely, V. Fock was an outstanding physicist as can be seen at

http://people.bu.edu/gorelik/Fock_ES-93_text.htm

He introduced the concept of *harmonic coordinates* x^{λ} satisfying

D^{κ}D_{κ} x^{λ} = 0
(λ= 0, 1, 2, 3).

where D^{κ}D_{κ} denotes the *covariant* d'Alembertian.

However, just these ''harmonic coordinates'', though surely being of some theoretical value,
had less success in practical problems. For instance, all coordinates with *spherical symmetry*
characterized by a metric of the form

ds˛ = g_{tt} dt˛ + 2 g_{tr} dtdr + g_{rr} dr˛ +
r˛ (dθ˛ + sin˛θ dφ˛) ,

where g_{tt}g_{rr}−g_{tr}˛ is *independent
of the angular coordinates,
fail to be harmonic* as can easily be shown by checking the
well-known criterion

∂_{κ} (g^{½}g^{κλ}) = 0 .

Take λ = 2 ~ θ to obtain

∂_{θ} (g^{½}g^{θθ}) =
(g_{tt}g_{rr}−g_{tr}˛)^{½}
∂_{θ} sinθ ≠ 0 ,

which is especially fulfilled by the Schwarzschild coordinates.

Seeing forward to your response with *precise information* about your sources.
Otherwise any further discussion will be useless.

Best regards

Gerhard W. Bruhn