Interpreting solutions with nontrivial Killing groups in general relativity

Letters from and to the editor of IJMPD

2009, November 22

Dear Professor Antoci,

I am not a general relativist. However, I found reading of your "The group aspect in the physical interpretation of general relativity theory" (Co-authored Dierck-Ekkehard Liebscher) thought provoking. I would like to see your ideas expanded and made accessible to every PhD-level student of physics. Would you, possibly with your collaborator(s), consider writing such a paper for the December 2010 Special Issue of Int. J. Mod. Phys. D (IJMPD).

Ideally, such a paper should be self contained. Or, any of the assertion/results that are invoked must be readily accessible in a publication at essentially the same level as your own paper. If this turns out to be difficult, you may consider presenting an extended addendum in a separate paper in a later issue of IJMPD.

If you agree and accept my invitation I would need from you a list of suggested referees, and a thorough discussion of the concerns raised by Malcolm A.H. MacCallum in Gen. Rel. Grav.38:1887-1899,2006.

You may have up to 50 pages of IJMPD. Your paper, if accepted for publication, shall be printed under 'Invited Reviews and Papers'. The deadline for the final draft to arrive my offices is 30 July 2010.

I hope you find this invitation of interest. I await your disposition.

Sincerely yours,

Dharam Ahluwalia
Special Papers Editor, IJMPD
Senior Lecturer (Editor, IJMPD, MPLA, IJMPA)
Department of Physics and Astronomy
Rutherford Building
University of Canterbury, Private Bag 4800
Christchurch 8020, New Zealand

2009, November 25

Dear Dr. Dharam Vir Ahluwalia,

please, forgive me for not answering earlier to your very kind invitation. My delay was not due to some hesitation, but to a short holiday in my beloved Venice. As soon as I found your mail, I contacted Professor Ekkehard Liebscher, who lives in Potsdam, and whose collaboration in the studies of general relativity was crucial in stating our early findings, ten years ago, and in understanding later that those early findings were not just occasional remarks on a particular solution to the field equations of general relativity. Our present understanding has rather emerged as a general viewpoint in the interpretation of that theory, based on two early, seminal works by Erich Kretschmann (1917) and by Emmy Noether (1918).

The manuscript now present in the Cornell Archive, entitled ``The group aspect in the physical interpretation of general relativity theory'', that drew your attention at ``thought provoking'', was written by us only under the invitation by an editor, Frank Columbus. As such, that manuscript is now promised for publication as a chapter in a book by Nova Publishers, hopefully in the first quarter of 2010. Both Professor Liebscher and the present writer, however, are completely aware that their work is not over, and that further study of the papers by Kretschmann, Klein and Noether in the years 1915-1918 is necessary to further develop the present understanding. Therefore, we shall work further till the beginning of July 2010, in order to comply both with the requirements needed to meet the readership that you have in mind in your invitation, and to obtain the accomplishment of our own theoretical goals. In particular, I shall devote my efforts to such goals, meant as the ones of a present-day theoretical physicist that still draws his inspiration from the ideas that where deeply debated during the development of general relativity, and have inadvertently settled like mere habits of mind in later times. By the beginning of July 2010, a list of referees will be provided too. It is not our intention, however, to enter a personal discussion with Professor Malcolm A.H. MacCallum about the concerns raised by him in Gen. Rel. Grav *38*, 1887-1899 (2006). We refrain, like we did in the past, from any sort of ad personam rebuttal. Otherwise, we risk to enter a sort of eristic dialectic (see Schopenhauer's ``der Kunst, Recht zu behalten'') on particular issues, while forgetting to strengthen and to enlighten the general character of the group theoretical interpretation of general relativity that we have adopted, from which the interpretation of particular solutions with a nontrivial Killing structure immediately stems in particular cases. It is our opinion that, once the general viewpoint by Kretschmann and by Noether is understood and accepted by the reader, its consequences will be accepted too like corollaries, no matter how momentous and debatable they may look to a reader not yet aware of the above mentioned, general viewpoint. We therefore aim at providing you with a deepened account of our former group-theoretical inquiry by the beginning of July, as promised.

Many thanks again for your invitation. All the best.

Salvatore Antoci

2009, November 26

Dear Professor Antoci,

Personally, I think scholarship has suffered under uncritical acceptance of many of our theoretical foundations. This is even more true for relativity; or, so at least it appears to me.

So, your work with Professor Liebscher carries a refreshing feeling and for that reason your acceptance of my invitation is greatly appreciated.

I have also found that Schopenhauer's book that you mention has an English translation. I hope to read it soon. Thanks for the reference, which in this instance is highly relevant to me.

I look forward to receiving your manuscript for IJMPD, perhaps jointly with Professor Liebscher.

With my best wishes,
Dharam Ahluwalia

2010, April 28

Dear Professor Ahluwalia,

please find enclosed the Latex file and the figures for the paper entitled "Interpreting solutions with nontrivial Killing groups in general relativity" by Dierck-Ekkehard Liebscher and by me. The paper has been written by availing of the AMS style file, but a version complying with the requirements of IJMPD will be available if and when the paper will be accepted for publication. We have tried to closely follow your suggestion, according to which you would like to see our ideas expanded and made accessible to every PhD-level student of physics. On the other side, it is our conviction that by adhering to the ideas of Klein, Kretschmann and Noether a general interpretation of both the special and the general theory or relativity emerges, that is necessarily expressed by the invariance properties of the metric against Lie "Mitschleppen". In our viewpoint, particular results, however interesting in themselves, automatically develop like corollaries from the adherence to the general interpretation. By combining your pedagogic suggestion with our viewpoint, we limited the discussion of particular examples, that was multifarious and review-article-like in our previous paper to just one simple, pedagogic example. We discuss here what happens when the choice of the vacuum manifold originally done by Karl Schwarzschild in 1916 is examined with due attention to its peculiar Killing group structure, and what pathologies and singular behaviours come out when the above mentioned structure is overlooked in the choice of the manifold. You have asked me to provide a list of referees. Please find the four following names and e-mail addresses:

Lluís Bel,
Fred Cooperstock,
Vladimir Dzhunushaliev,
Hans-Juergen Schmidt.

I am most grateful for your very kind invitation and stay,
Yours sincerely,

Salvatore Antoci

2010, November 5

Dear Professors Antoci and Liebscher,

Below I attach a referee report for your kind consideration. Please revise your manuscript following referee's suggestions and concerns and send it back to me asap.

Best regards,
D. V. Ahluwalia
Special Papers Editor, IJMPD

----------------------------------- Referee Report on "Interpreting Solutions with nontrivial Killing group in general relativity" by S. Antoci and D-E Liebscher. ...................................

The present paper adds a good deal of knowledge to the history of relativity theory and is worth being published. Especially, literature which was originally in German language, and is not always translated up to now, is cited. Unfortunately, a large number of German words now appear in the text, and the non-German reader might be frustrated to read "Mitschleppen" without translation, one could at least say: it is the noun related to the verb "lug" in English, but "luggage" would only roughly meet the German meaning of it. Also, I would advise in this special case, that for all papers from old journals the complete titles both in original and in english language be given, as these papers are not easy to find in typical libraries.

However, I have a great problem with chapter 6: Already M. MacCallum in GRG 38 (2006) 1887, see also gr-qc/0608033, wrote a paper where he critizised Antoci and Liebscher, e.g. for using the word "singularity" in a sense differently from its typical use in the field. Even if this critizism may be a little bit too harsh, I think, they should at least cite it, as it refers to the same topic as chapter 6 of the present paper. When they write (page 9, 10 lines from below): "One cannot accept ... invariant quantity ...may diverge somewhere...", then this is against usual interpretation. Example: 1/R, the inverse of the scalar curvature, is obviously an invariant quantity and diverges in empty spacetime; of course, regions of spacetime, where 1/R changes from positive to negative values, do not have any special property. This is just the same with the invariant parameter alpha in eq.(6.4). So, the calculations seem correct, but the interpretation in this case is simply wrong, even if Karl Schwarzschild in 1916 might have been debated in this way, too.

Section 6 must either be completely deleted, or edited greatly to completely remove the confusion. ____________________________________________________________________

2010, November 7

Dear Professor Ahluwalia,

thank you for your letter. We changed the article in each point noted by the referee, i.e.

we dropped the interpretation "singularity" in section 6 with the citation of MacCallum's paper exactly as the referee proposed,

we added the full titles of each cited paper and added for the purely English reader translations of the titles which are not in English,

and we added an english explanation for german words in the text.

Best regards


2010, November 9

Dear Professor Liebscher and Professor Antoci,

Thank you for your e-mail and for sending the revised draft. I have passed through the manuscript through the referee, and sought additional advice. It is the recommendation of my referees¹ that while reference to MacCallum should be retained, Sections 6 and 7 distract from the main argument and, in fact, hurts your main argument advanced in Sections 1-5. I agree with this assessment.

Would you, therefore, be so kind as to revise the manuscript accordingly. I would very much like the revised draft to meet the approaching deadline to close the December Special Issue of IJMPD. For this reason your prompt attention would be most helpful.

Best regards,

D. V. Ahluwalia
Special Papers Editor, IJMPD

2010, November 16

Dear professor Ahluwalia,

thank you for your letter. We are happy to see that the referee now has no more objective objections. His new claim that the sections 6 and 7 would distract from the main argument cannot be accepted. These sections are -- in our view -- exemplifications of the main argument, which happily enough exist in the simple case of the Schwarzschild field.

We are aware of that the facts which we exhibit do not fit the standard expectation. Of course, it is not necessary to call these by words (like singularity) which have in General Relativity a more specialised meaning than in everyday use. Therefore we followed the request to drop the interpretion by these notions. Words are hollow shells.

No referee objected the calculations, which are simple enough. The diverging values of the acceleration in a very simple case exist, and they are measureable in principle without any trick. Sections 6 and 7 are corollaries to 1 by 5, and no distraction. In his first statement the referee admitted just the same, namely that the line of section 6 is like the one Schwarzschild used.

Consequently, we will not change the text.

We are really sorry to be forced to put you in a worried position. If you feel not to publish the present article because one of the referees feels that sections 6 and 7 distract from the main argument, so just drop it.

With full acknowledgement of the troubles you take

Sincerely yours


1. The value of 1/R, which was cited by the referee as a quantity similar to the acceleration in question, is of a truely different type, because R is the measured quantity, not 1/R. If one could get rid of diverging values just by only switching the attention to the reciprocals as the referee proposes, that would help in any place. However, 1/R nowhere couples to equations of motion, while R does. Therefore it is the zeros of 1/R which matter (i.e. which are measurable), not the zeros of R.
2. Whether one must, or has to, or should consider the horizon to be a singularity or not depends on the personal point of view. When one is happy about the possibility to continue analytically across the horizons, the answer is clearly no. We do not insist to preach our point of view, that physical measurements (direct or indirect) should decide. The numerical attempts to solve the evolution of binary black holes decided already not to consider any interior.

Sincerely yours,

Dierck-Ekkehard Liebscher

That was, of course, the end of the story.