I am sorry but I did not read the help on linking sites so I give the the [link: http://people.sissa.it/~rezzolla/lnotes/virgo/node9.html] once more. Sorry, the rest of the text is linked to the site.

Dear Dan,

yes, I confirm you that, exactly like the FQXi, the Gravity Research Foundation has a remarkable merit system. What is really important for them is the quality of the research. When I received an Honorable Mention in the 2009 Competition I had no academic affiliation too.

I well know that the entry deadline is April 1, I am going to attend this year too. Together with some collegues, we are finishing an Essay on black holes exactly like you.

Best wishes for this Competition too.

Cheers,

Ch.

Dear Jacek,

the sentence that you quoted by the paper of Rezzolla reads:

"... it is not easy to predict that there exist solutions behaving as waves."

which is different from:

"... it is impossible to predict that there exist solutions behaving as waves."

In fact, such solutions of exact equations have been found, see for example

H. Bondi, F.A.E. Pirani, and I. Robinson, Proc. R. Soc. London A 251, 519 (1959);

H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact solutions of Einstein's field equations, 2nd ed. (Cambridge Univ. Press, Cambridge, 2003) Secs. 24 and 31;

J. Ehlers and W. Kundt, Exact solutions of the gravitational field equations, in: "Gravitation: an introduction to current research", ed. by L. Witten (Wiley, New York, 1962);

Y. N. Obukhov, J.G. Pereira and G. F. Rubilar, Class. Quant. Grav. 26, 215014 (2009).

On the other hand, it is true that

"the concept of gravitational waves as solutions of (linearized) Einstein equations is valid only under some rather idealized assumptions such as: a vacuum and asymptotically flat spacetime and a linearized regime for the gravitational fields."

But, even if idealized, such assumptions can be realized with an excellent approximation. Take two neighbouring free-falling test masses within a vacuum cylinder in the Earth's gravitational field. For Einstein's equivalence principle they realize a vacuum and locally flat spacetime. This is EXACTLY the principle which is used for detect gravitational waves with interferometers. In fact, test masses suspended to pendulums represent an excellent approximation of free-falling test masses.

More, the linearized regime is an excellent approximation even for the gravitational field of the Solar System (historically Einstein used the linearized regime to test astrophysical predictions like the light deflection, the gravitational redshift and the precession of the Mercury's perihelion). The gravitational field of a gravitational wave is various order of magnitude lower than the gravitational field of the Solar System, thus, the linearized regime is an absolutely excellent approximation. In fact, high order terms are lower than 10^-42...

Best regards,

Ch.

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  • Post #33

Hello dear Dr Corda, Happy to see you again,good luck ,it's a beautiful essay,congratulations

Steve

Hi Steve,

nice to see you again too.

Thanks for congratulations, I see that you do not attend to the Essay Contest this year.

Cheers,

Ch.

Dear Christian,

I have not said it is impossible to predict that there exist solutions behaving as waves. If we try very hard... And it depends on assumptions. I have just assumed another scenario I will try to find another solutions.

I have only read the paper by Y. N. Obukhov, J.G. Pereira and G. F. Rubilar and found it interesting. They claim:

1. any exact gravitational wave solution is highly idealized, and is thus probably more of academic interest

2. As we have seen, the exact plane-wave solution of Einstein's equation transports neither energy nor momentum. This property appears to be quite unusual, since one could expect that a gravitational wave, like any other gravitational field configuration, should be characterized by nontrivial distribution of energy and momentum. In this sense the exact plane wave solution, although being mathematically well defined, appears to be a physical puzzle.

As you have maybe noticed in my concept e.g. the Earth is a gravitational wave orbiting the Sun along the geodesics. So it transports the energy and momentum and is not a physical puzzle. That is why I think it is worth further research. Maybe the idea is wrong but very simple and beautiful.

As far it has not been successful to detect gravitational waves with interferometers. I cannot be sure it is impossible. That is only a consequence of my concept.

Best regards,

Jacek

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  • Post #36

Hello,Christian

What is your opinion about alternative to intrinsic space-time curvature -intrinsic space curvature?

http://www.fqxi.org/community/forum/topic/946

Hi Yuri,

I see in your Essay that the first cited example of physical evidences supporting the Ratio 3:1 is the ratio 3 space-like dimensions - one time-like dimension. It is an interesting Essay, I wish you good luck.

Concerning your question, I think that the space-time should be globally and intrinsically curve.

Cheers,

Ch.

Dear Jacek,

in my paper Gen.Rel.Grav.40, 2201-2212 (2008) I released the hypothesis that the whole Dark Energy could be a cosmological gravitational wave. In that case, the frequency of the wave should be minor than the Hubble Constant. The model is consistent with both of the Hubble Law and the Cosmological Redshift.

Cheers,

Ch.

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  • Post #39

your discussion is relevant.

Dear Christian you say" I released the hypothesis that the whole Dark Energy could be a cosmological gravitational wave. In that case, the frequency of the wave should be minor than the Hubble Constant"

It's very relevant, do you consider this wave as the first wave?Could you develop a little please?

Reagrds

Steve

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  • Post #40

Hello dear Christian,

Thanks you are welcome.

No as habit I am bad organized lol, after all it's not important.You know I will publish probably in the future with a kind of team , humanistic and universal.I need a coach or others I don't know, in all case I am not skilling in management and administration.It's the life.I have problems to focus.But I continue to class all and improve the correlations.

Regards

Steev

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  • Post #41

Christian,

Congratulations on your accomplishment. Although by the appearance of your entry into this year's contest, it seems only a matter of time before you were given recognition.

I hope I am able to finish my essay, as it seems as if time is my worst adversary, nowadays. If not, so be it. There's always next year. Too many things to do and learn and not enough time.

Have a great day!

Dan

Hi Dan,

I am very honoured for your kind words, thanks a lot.

Maybe we could collaborate in the future.

Have a great day you too!

Cheers,

Ch.

Steve,

I applied Eqs. (3), (4) and (5) of my Essay in a cosmological framework. In particular, I released the strong assumption that the mass-energy (4) represents the Dark Energy of the Universe. In that case, the cosmological gravitational wave is the wave-packet (4). Then, the conformally flat line-element (15) becomes the analogous of the FRW line-element. The assumption of homogeneity and isotropy removes the z-dependence in (15). At the end I found consistence with both of the Hubble Law and the Cosmological Redshift.The fact that the frequency of the wave-packet (4) should be minor than the Hubble Constant implies that the length of the cosmological perturbation is longer than the Hubble Radius. This means that cosmological observations remain "frozen" with respect to the cosmological gravitational wave.

The pre-print of the paper is available in http://arxiv.org/abs/0802.2523

Cheers,

Ch.

Dear Christian,

I have found your papers to pioneer in the development of the promising and innovative GUT and the first that share my view on the dark matter and energy and on the other hand I feel you could make a few steps forward in the same direction. I am sorry for these words. I will try to explain.

I have just read your "oscillating universe" on arXive that you have recommended to Steve. I do not understand all the intricacies of the paper due to my partial incompetence in mathematics. I agree with the idea in general and the approach to oscillating universe in the expansion phase.

Are you acquainted with Sladkowski J. Strongly gravitating empty spaces. arXiv:gr-qc/9906037v1?

He writes: on some topologically trivial spaces there exist only "complicated" solutions to the Einstein equations. By this we mean that there may be no stationary cosmological model solutions and/or that empty space can gravitate. Such solutions are counterintuitive but we are aware of no physical principle that would require rejection of such spacetimes.

I fully agree. This is the step in the right direction.

However later on he writes: Suppose that space-time is only a secondary entity emerging as a result of interactions between physical (matter) fields.

And in this case I think it is vice versa.

Finally there is my point. Could you use your approach to the spacetime but make it scale invariant? I mean up to the h scale? I mean to elementary particles? And you should see all interactions unified. Maybe a GUT?

Best regards,

Jacek

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  • Post #45

Dear Dr. Corda,

I went thro' your lucid essay with ease and entusiasm.The theme of your essay is too clear.But what is perplexing for me is,what makes you shyaway from quantizing gravity/acceleration straight away and try to formulate successful theory of quantum-gravity sothat you can unify all four physical forces? For how to do it,please go through my essay and I hope you will find the solution there.So Iam interested to know how you react to my essay.

Best regards and wishing success in the competition.

Sreenath B N

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  • Post #46

Hello to both of you,

Thanks Christian.It's really interesting all that.I ask me also the real meaning of quazars for exampple.or how the photons rotates on the time line since the primorial dynamic.If these quazars are correlated with the expansion, let's assume a critic point of density where the contraction begins.

Is it possible to detect this point if we take the ancient rotations of spherical volumes(now of course it's perhaps in the future).The decalage in the red is relevant if the rotations around an universal center and around many centers are inserted.

I think really that spherical volumes increasing towards the center are very important.In fact these galaxies and super groups and mega groups ...can be classed in their pure evolution, logically the mass increases and we can thus see also the frequences of hv.But only if a topological spherical universe, closed and evolutive is inserted with its evolution.In logic we could see the acceleration, deceleration, critic point, acceleration, deceleartion, equilibrium point (mass) the gravitational wves correlated with rotating spheres(quantic and cosmologic) are relevant atmy humble opinion, if we consider the uniqueness and its entropy, thus the number seems important in its pure finite universal serie of decreasing of volumes.If we link with the classments of hubble, we can see the evolution of rotations of spheres and thus the spherization.The volumes seem a key for a classment of gropus and super groups....and the center the biggest volume.

Best Regards

Steve

Dear Sreenath,

thanks for your comment.

Actually, I am shyaway from quantizing gravity because I do not know which is the correct classical theory to be quantized. Is it standard General Relativity or is it an Extended Theory which takes into account the presence of an intrinsic space-time curvature in our Universe? I hope that gravity-waves observations will permit, in the future, to clarify this issue.

Notice that this point could modified the values of both the force of quantum gravity and the Constant of Quantum Gravity that you cited in your Essay.

Wishing success in the competition to you too.

Cheers,

Ch.

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  • Post #48

Christian,

You have flattered me with your offer. Although, I'm not exactly sure what a novice like me could offer the partnership other than some good ideas. I'm sure that you have forgotten more physics than I ever knew! :) I do believe in my cosmological model and I have a few other deeply held, yet undoubtably controversial views, but as I told Jason Wolfe on one of the blog forums, you can't change the world without at least a little controversy now and then.

Cheers,

Dan