Dear Vladimir Onoochin,

the mechanism was explained by Hulse and Taylor 1981

A NEW TEST OF GENERAL RELATIVITY: GRAVITATIONAL RADIATION AND

THE BINARY PULSAR PSR 1913+16.

what is called "potential energy" is actually a maximum of the energy of the system of the two neutron stars. In a more simple system, with smaller masses, all the potential energy is transformed in kinetic energy prior collision. In this case where huge masses are involved, the kinetic energy is depleted and radiated away in form of gravitational radiation prior collision.

The amount of kinetic energy which was missing was calculated to be the same as the radiated energy.

It is the vacuum energy which provides what is called potential energy...

after the collision the energy of the system is simply lower than before but cannot be negative...

Dear Stefano Quattrini ,

I cannot find the paper of Hulse and Taylor of 1981 but I found the paper of Taylor and Weisberg? A new test of general relativity: gravitational radiation and the binary pulsar PSR 1913+16

Its content is of some interest.

For example, the authors write (p. 910)

'The model explicitly includes relativistic terms whose amplitudes vary periodically with orbital phase—gravitational redshift, transverse Doppler shift, post-Newtonian corrections to the elliptical orbit, and gravitational propagation delay —as well as secular relativistic terms involving advance of periastron and orbital period change due to emission of gravitational radiation. The model is formulated on the assumption that general relativity is the “correct” theory of gravity, or at least has adequate accuracy for calculating the terms mentioned above; such accuracy is ensured, for all except the gravitational radiation term, by a number of high-precision tests within the solar system.'

So after the data obtained from the radio signal the authors reconstruct five 'measureable' parameters - and it seems the accepted the rest two parameters needed to calculate the complete motion of the cosmic bodies - and obtained excellent correspondence to the general relativity.

How many tests of confirmation of the GR within the solar system have been known to 1982?

If one translates the high scientific text of the authors into ordinary languages, one has that if the GR is correct, then it is correct.

The other interesting point is that now everybody knows: binary pulsar PSR 1913+16 is a binary star system composed of a neutron star and a pulsar. It is known just from the paper of Taylor and Weisberg. But the authors make such a conclusion because it is 'highly likely' (their discussion in Appendix A). So we have wonderful example of transformation of assumption into firmly confirmed scientific fact.

But my question is not on change of periastron in the pulsar PSR 1913+16 - this change does not mean that this binary system loses its energy due to the gravitational radiation. Too few experimental data are to make such a conclusion.

My question is: if the binary stars lose their energy due to the gravitational radiation, what force acts on the stars and decelerates their motion?

Dear Vladimir Onoochin ,

yes the paper if from Taylor and Weisberg. Hulse did a similar work and won the Nobel prize with Taylor.

it is not a rosetta trajectory, in which the periastron changes its positions but goes back to the the original after a certain timer, there is instead a decay towards the center of mass of the binary.

the observed decay of the orbit at page 914,915 is consistent with the loos of energy through the emission of gravitational radiation as predicted by GR (8)

The force is the back-reaction of the "energetic back ground" which emits gravitational radiation .

Dear Stefano Quattrini ,

Taylor and Weisberg use Peters and Mathews' expressions to estimate the decay of the pulsar orbit (according to the model used by them to calculate this decay from some parameters of the radio signal). Unfortunately, it is impossible to check if this decay will go to the collapse of the bodies of this two-body system. Maybe due to precession the orbit of the pulsar will change and the ray of the signal will leave the solar system.

But again my question is what force which decelerates the bodies of PSR 1913+16?

It is known so called satellite paradox when the satellite falls to the Earth in spiral orbit and due to the drag force its velocity increases. But this force is well known, it is the friction of molecules of the air at an altitude of the satellite orbit. This drag force is tangential, therefore the orbit of the satellite is of spiral type.

For the pulsar, such a tangential force is absent.

The equations given in the paper of Peters and Mathews, in the textbook of Landau and Lifshitz say nothing on possible force. These equations are written for the metric. Even we assume that perturbation of the metric rotates with the body, the 'acceleration' of this perturbation is directed toward the baricenter of the system. So the force of reaction should be directed out of the system.

In celestial mechanics it corresponds to the case of transfer of the satellite to the higher orbit and the period of rotation increases. If one applies these arguments to motion of the pulsar, it would mean that the radius of the orbit should increase and the instead of the periastron advance we shuld observe opposite process.

One more puzzle. It is accepted by some scientists that the stars are formed from protodisks and most of stars are initially formed as binary or many-body systems. The single stars (a half of all stars in the unverse) are obtained from dissolution of the binary systems. In the other words, their orbits were doing larger and larger until they leave each others.

But according to the GR - if the stars lose their energries - all binary stars should have the orbit decay unti their collapses. We don't observe collapses of the stars. If ot occurs, it is more or less rare event.

So the effect of dissolution of the binary stars contradicts to the loss of the energy due to the gravitational radiation.

Dear Vladimir Onoochin

I always thought that the orbits of planets around a star, planetary disks and accretion disks are well understood and mathematically proved. But recent observations that are not in line with the models (e.g. the Roche limit) show that I was a bit naive.

What I know for sure – although I haven’t yet published a paper about it – is that gravity influences the direction of the transfer of free energy (quanta) in vacuum space. An example is the well known curve of Keppler’s diagram of the mean velocity and mean distance of the orbits of the planets within our solar system. Thus in our solar system not only the planets have their orbit around the sun, all the quanta transfer in vacuum space has a resultant motion that “moves” like an enormous disk with the sun in the centre. The resultant velocity of the quanta increases in the direction of the centre, in line with Keppler’s diagram.

The consequence is that if I “drop” a molecule somewhere in vacuum space around a lonely star the molecule will move to an “orbit” where the local resultant motion of the quanta of the electromagnetic field is equal to the motion of the molecule, because of its mass (energy content).

But in a binary configuration of 2 celestial bodies, there is no matter in the centre of vacuum space around. Thus both celestial bodies are constantly “merging” their corresponding disks of resultant motion of free energy, created by their respective gravitational field.

A free quantum of energy (Planck’s constant) has momentum too. Thus the continuous merging of the 2 disks of resultant motion is only possible if there is a supply of energy. The only source of energy are the 2 celestial bodies thus we observe a loss of energy in relation to the rotational velocity of both celestial bodies. This is an acceptable explanation if you use phenomenological physics (no matter the origin of gravity).

Now a more insightful explanation.

A celestial body is a huge concentration of energy in vacuum space. But once, the energy was free energy of the electromagnetic field in vacuum space. Thus the celestial body is a local surplus of energy at the cost of a deficit of energy in vacuum space around. Thus the celestial body and vacuum space around are a “duality”. The surplus of energy of the celestial body is equal to the amount of energy in vacuum space that is a deficit. If we change the energy of the celestial body, vacuum space around will accommodate correspndingly.

If we increase the energy in vacuum space around – less deficit – the surplus of energy of the celestial body must decrease too because of both universal conservation laws: energy and momentum. Both universal conservation laws represent the properties of the electromagnetic field (universal electric field is the energy part and the magnetic field is the vector part).

The tragic of Albert Einstein is that he described the universal electric field in his theory of General relativity, although he was convinced that he described the force of gravity. But gravity is a vector force, in line with Newton’s theory of gravitation (instantaneous influence). See: Tom Van Flandern (1998); “The speed of gravity – What the experiments say”. Physics Letters A, 250: 1 – 11 (https://doi.org/10.1016/S0375-9601(98)00650-1). Thus the proposed gravitational waves are gravitational induced electromagnetic waves.

With kind regards, Sydney

Dear Sydney Ernest Grimm,

After publishing Van Flandern's paper it was some discussion if the finiteness of the speed of gravity can go to the loss of stability of the Solar system. I took a part in this discussion and as I remember both sides of this discussion couldn't convince opponents that they are right. The relativists had to reply to Van Flandern since he had some authority among astronomical society.

I remember too that Van Flandern followed a theory of gravity developed by Le Sage. Le Sage developed his theory in XVIII century and he couldn't know about the EM waves. But maybe the fluxes of LeSage's 'gravitons' are some kind of the EM interaction.

I suppose that your idea is close to La Sage's concept.

The question is how to detect these 'gravitons' and how to separate them from ordinary EM interaction. Until now there are no evidences that the neutral mass can create the EM waves.

With the best wishes,

Vladimir

Dear Vladimir Onoochin

The long range gravitational vectors are superpositioned on the short range vectors of the magnetic field. Thus the force of gravity influences the universal electric field in a direct way (the freedom of the direction of the motion of the quanta of energy).

There is experimental evidence:

• Louis Rancourt and Philip J. Tattersall: "Further Experiments Demonstrating the Effect of Light on Gravitation". Applied Physics Research; Vol. 7, No. 4; 2015 http://dx.doi.org/10.5539/apr.v7n4p4
• Chungpin Hovering Liao (2019), “Microwave-caused influence on gravitational constant G in Newton’s gravitational law”. DOI: 10.13140/RG.2.2.15509.37600

The cause behind gravitation is the vectorization of the scalars of the flat Higgs in vacuum space around the rest mass (Higgs mechanism). I am afraid that the vague concepts from the XVIII century are not well suited for modern physics.

With kind regards, Sydney

Dear Rana Hamza Shakil

I agree that some factors of the energy loss exist. But my question is

what force of reaction which decelerates the binary stars when the latter emit the gravitational waves?

And one more question remains

why the wide binary stars - instead of the orbit decay - have a trend to transform to two single stars?

All factors you mention should give the orbit decay. What factor gives the dissolution of the binary systems?

I agree that interaction of the external bodies can give such a dissolution. But it is more or less rare event and it cannot give dissolution of a lot of binary stars.

I hope my question is physical. The general relativity can be excellent theory but it cannot be reduced to a number of formulas.

Dear Vladimir Onoochin ,

it will, since the center of the masses of the two stars were progressively approaching although slowly. Their increase of kinetic energy did not justify at all the variation of potential energy due to gravitation.

there is no paradox, the friction force makes its kinetics decrease a bit such that the satellite passes to a lower orbit gaining a lot more kinetic energy with higher and higher energy losses due to increase speed and increase air density.

The energy in that case is lost by friction (thermalized with emission also of EM waves). For big bodies which oscillate, there is a back reaction of the background which slows down their speed increase (compared to the expected) with a production of gravitational waves.

Dear Stefano Quattrini ,

The satellite paradox has been explained in 1950th:

B. D. Mills, Satellite paradox. Am. J. Phys. Vol. 27, p.115 (1959)

But in this paradox direction of the decelerating force is well defined - tangentially to the orbit.

My question is what the reaction force due to emission of the gravitational waves is directed.

The situation is similar to the puzzle of stability of the electrons in Reserford's model. Now a discussion on stability of the electron has been forgotten. But some papers of such authors as Schott, Darwin published works where the explanation of the stability(of the absence of radiation is given within the classical electrodynamics. But the authors tried to prove that under some conditions the radiation is absent.

In the binary stars system, it is stated that the radiation exists with sure. So what we need is to determine the radiation force and the direction of this force. In typical system of binary stars, these stars don't oscillate. The power of radiation should depend on the acceleration of the body. This acceleration is directed toward the baricenter. A direction of the radiation force?

With the best regards,

Vladimir

Dear Vladimir, Vladimir Onoochin

actually there is no force if there is no object to apply to, it is a wave which transmit energy hence it makes work on object by displacing them around a fix position. That is what was registered by the arms of the LIGO / VIRGO interferometers.

The background receives part of the energy of the binary stars which have a sort of "dipole oscillation" and radiates it away in form of gravitational waves.

Dear Stefano Quattrini ,

> actually there is no force if there is no object to apply to,

It is not completely so. In a paper of Postnov and Yungelson, The Evolution of Compact Binary Star Systems. Living Rev. Relativity, 17, (2014), 3, the authors write on the back reaction - but only in the title of one subsection. No any explanation what is this misterious back reaction.

One can understand from the content of this paper that the emission of gravitational waves is one of the main factors of the orbit decay of compact binary stars. But it doesn't resolve a puzzle - what is this back reaction force.

With the best wishes,

Vladimir

Let's see what Gary Nash has to tell you about it...

Dear Stefano. Yes, MGR does have something to say about this issue. In "Modified General Relativity and dark matter" it is shown how the line element vector field is a fundamental part of the Lorentzian metric and satisfies the spin-1 Klein-Gordon (KG) equation. That links the spin-1 field with gravity in a Lorentzian spacetime. The KG equation is □Xβ = k2Xβ+Jβ with a current Jβ. When the particle "mass" k vanishes as in electrodynamics, ∇αKαβ=2Jβ-∇α˜Ψαβ where ˜Ψαβ = ∇αXβ +∇βXα = £Xgαβ and £Xgαβ is the Lie derivative of the metric. It tells us how fast the metric travels along the flow of the vector field X. From the KG equation we get the modified Maxwell equation as stated. Outside of the star where there is no current, the flux of the flow of the metric or the flux of part of the energy-momentum of the gravitational field (since Φαβ = 1/2£Xgαβ + £X(uαuβ) absorbs the radiation from ∇αKαβ.

Gary Nash,

Your post says nothing about a force which decelerates the star emitting the gravitational energy.

The equations describing the emission of these wave are known. What is the force that is analogue of the back reaction force in classical electrodynamics?

Can you give the expression for this force in post-Newtonian approximation? It is sufficient to consider this approximation since the effect of gravitational waves is caused by the finiteness of the speed of gravity. The correct expansion of Einstein equations with respect to c_g, the speed of gravity, gives post-Newtonian approximation.

Vladimir-Onoochin As I assume you know, gravity in GR is described geometrically; there are no gravitational forces involved . MGR is linked to electrodynamics, which is described geometrically as shown. The Lie derivative of the metric links the energy-momentum of the gravitational field to the modified Maxwell equation.

To get at your original question, it was unclear to me about what radiation you were talking about; gravitational or electromagnetic or both. From your comment I now see that you are looking for an explanation of the gravitational radiation from the binary star system. That will follow from a study of gravitational waves in MGR. There, the wave equation is inhomogeneous with the RHS involving the Lie derivative of the metric. The solution for the weak-field hαβ will involve the retarded solution of the inhomogeneous wave equation. Gravitational waves in MGR move at speed c just as they do in GR, but now the flow of the metric along the vector X is involved. The gravitational radiation from the stars is accounted for in the change of the metric of spacetime. Again, this is a geometrical explanation of the event as there are no gravitational forces per se in GR/MGR. I have not worked out the details of the gravitational energy loss of binary stars but they would follow from this discussion.

Gary Nash ,

> gravity in GR is described geometrically; there are no gravitational forces involved .

If you read all posts of this discussion, you can find that I don't ask about origin of the gravitational force. For people accepted the GR, this force is the gradient of the curved space, for people following other theories of gravitation it is something else. But my question is:

what is the physical force which acts on the physical body - the star - and which decelerates the motion of the latter?

I don't need in information on the wave equation for the metric. I wish to understand how the binary stars loose their energies - the relativists treat advance of their periastron as the orbit decays and these decays are caused by the loss of the energy - like in the satellite paradox. The basic equation for the satellite paradox is

dE/dt = v*F

where F is the drag force.

The stars are very physical bodies so what is the physical force which decelerates them?

Vladimir Onoochin, you are looking for a solution to the problem from a Newtonian point of view. Gravity is much more complicated than that. Good luck with your approach.

Gary Nash ,

In the Newtonian mechanics, the gravitational waves are absent so I don't seek this 'Newtonian solution' of loss of the energy. But this problem should have solution in post-Newtonian approximation, the only accessible approximation in the GR.

Vladimir Onoochin, you are mincing words as the post-Newtonian approach involves a small perturbation in the flat spacetime of Newtonian physics, which provides for the existence of gravitational waves; in other words, a Newtonian point of view. I did not suggest to use Newtonian physics! Post Newtonian physics certainly does not involve the line element field, which is a fundamental part of all Lorentzian metrics. If you want to explain the change in gravitational energy loss, you need to use all of the mathematics that are involved in the description of gravity, dark matter and dark energy. GR doesn't have that capability without the addition of dark matter profiles and the first order implication of the cosmological constant to represent dark energy. With for your approach, you won't find what you are looking for because GR has no tensor that describes the energy-momentum of the gravitational field.

Gary Nash ,

The expressions for the gravitational radiation power have been derived still in 1963 by Peters and Mathews - without dark matter and dark energy - using the expressions given in the textbook of Landau and Lifshitz. All astrophysicists use the expressions of these authors. But I ask about the back reaction force. This force cannot be derived from the metric, it is the force which should act on the material body.

Vladimir Onoochin, I know what has been done and what has not. As stated for the last time, invoking the line element field is necessary to have the extra freedom to construct a tensor that describes the energy-momentum of the gravitational field. You are incensed with forces instead of learning that gravity and its associated phenomena are described geometrically. If you don't get that, go find your "back reaction force" from your perturbed flat spacetime. You say "...This force cannot be derived from the metric". That may be true for a Riemannian metric but not for a Lorentzian metric, which exists because of the line element field. I won't respond to you until you learn some differential geometry. Best of luck.

1) Gravitational radiation. As the stars orbit each other, they emit gravitational waves that carry away energy from the system. This causes the stars to gradually spiral inward toward each other, eventually leading to their merger.

2) Tidal dissipation. The gravitational forces between the stars cause them to deform slightly, which results in the conversion of some of their kinetic energy into heat. This heat is then radiated away, causing the stars to lose energy and spiral inward.

3) Magnetic braking.

If one of the stars has a strong magnetic field, it can interact with the other star's magnetic field, which also results in energy loss and spiral rotation.

If we don’t solve the problem about the nature of the force of gravitation, a lot of physics will be unsolvable. Not only in macroscopic reality but also in microcosm. Because gravity emerges at the moment that matter is created by/from the electromagnetic field. That means that the quark/gluon model (high energy physics) involves gravitational influence but we cannot recognize it.

In quantum theory space is detectable because there are spatial “categories” and each “category” consist of equal type of properties. We have termed these “categories” fields and every basic quantum field has distinguishable properties. 3D Scalar property (Higgs field), 1D vector property (magnetic field) and 3D topological transformations (electric field, responsible for the quantum of energy and the constant speed of light).

The problem with gravity as an emergent force field is that gravity cannot have a basic quantum field of its own. If a theorist propose the existence of a second 3D topological quantum field – dedicated to gravity and corresponding with the ideas of Einstein – there are no arguments why this hypothetical gravitational field is separated from the structure of the electric field.

The consequence is that gravitational waves don’t exist because gravity has no basic quantum field of its own. Thus gravitational waves as a back reaction are a type of local deformations of the structure of the electromagnetic field, generated by the gravitational field of both celestial bodies.

Unfortunately it is nearly impossible to discuss the nature of gravitation because it seems to be some kind of a religion. At least for physicists.

With kind regards, Sydney

Gary Nash ,

I asked a question in a very clear form:

What is the back reaction force acting on a material body, a binary star.

You have uploaded a number of posts about 'metric flow', 'dark matter', 'dark energy', 'big bang' etc but not about forces.

I think you don't understand the subject of this discussion. Therefore, I don't need your advices to learn geometry

Vladimir Onoochin: On the contrary, if you knew some differential geometry, you could understand the difference between a Lorentzian metric and a Riemannian metric. A Lorentzian metric exists because of the line element vector field, which provides that metric with the flexibility to describe dark energy and dark matter. The line element vector field also belongs to the spin-1 KG wave equation and therefore electrodynamics, which is linked to gravity by the Lie derivative of the metric. MGR is the only extended theory of gravity that has a symmetric tensor that represents the energy-momentum tensor of the gravitational field. When one talks about the loss of gravitational energy from a star system, the loss of gravitational energy-momentum is paramount, which is described by \Phi-ab.

What you obviously do not understand is gravity, which is described by differential geometry. You talk about gravitational waves without having any knowledge about where the weak-field equation \square h_ab=0 comes from. I pointed out to you in MGR that equation is no longer homogeneous because \Phi_ab is now fundamentally present. Gravitational waves still travel at the speed of light from the retarded solution, but the magnitude of the waves depend on the Lie derivative of the metric.

Thus, to study the loss of grav. en-momentum from any system, the study is fundamentally geometrical. There are no forces in GR/MGR; spacetime is curved and that governs how bodies move in spacetime. You shouldn't ask any question on forces depending on gravity until you understand GR and then MGR.

Dear Sidney Grimm. If you have followed the development of "Modified General Relativity and quantum theory in curved spacetime" (Int.J.Mod.Phys A 2021), you will realize how QT is linked to gravity in MGR by the Lie derivative of the metric. The line element vector field (X,-X) is a 1-D subspace of the tangent space and exists at every point in spacetime. A Lorentzian metric does not exist without the line element field. One of the pair of regular vectors in that field acts as a fundamental quantum vector because it satisfies the spin-1 Klein-Gordon wave equation that is the equation of motion of spin-1 particles. In order to get a wave equation for that spin in curved spacetime, where covariant derivatives do not commute, it is necessary to symmetrize the asymmetric spin-1 equation. That introduces a symmetric tensor into QT, the Lie derivative of the metric, that has been ignored in QT.

Thus, gravity does have a "basic quantum field of its own" and gravitational waves certainly do exist.

Gary Nash,

First of all, don't dictate me to study MGR. There are many different modifications of GR. So far, all of them do not have a solid experimental verification. Thus, all these MGRs are at the level of some of the proposals of their authors.

Second, I have given enough references to works on gravitational waves that are well accepted by the mainstream. For example, Nobel Prize winners cite these works. Their authority is sufficient to use the expressions given in the cited works.

Third, some forces are acting on the binary stars. The drage force, force due to mass exchange, etc. But none of the authors who mention these forces in their works writes that these forces should be calculated using differential geometry.

Fourth, my question is formulated in a clear form: what is the mechanical force acting on the mechanical model (since the binary star is a mechanical body) as a reaction to the emitted gravitational waves.

I do not need to know the abstract consideration that "metric change....". If such a "metric change" occurs, it cannot be verified because the effect is too small, of the order of (v/c) ^5, that is, inaccessible to modern measuring instruments. But the force of the back reaction - if the assumptions of GR are correct - should be quite large, since the advances of the pulsar periaster have been detected.

Vladimir Onoochin: If I were you I would be very embarrassed to state: "There are many different modifications of GR. So far, all of them do not have a solid experimental verification. Thus, all these MGRs are at the level of some of the proposals of their authors." If you had the ability to read and understand the 42 pages of "Modified General Relativity and dark matter" Int. J. Mod. Phys D 2023 32 6 you would see the detailed calculations of many cosmic events and how MGR beautifully describes them without any addition of dark matter profiles that GR requires. The extra freedom of the line element field in a Lorentzian spacetime describes dark energy and dark matter. That vector field also unifies the spin-1 field with gravity through the Lorentzian metric.

Some people are just too stubborn or incapable to learn new things in order to participate in a reasonable conversation. You are one of them and I won't be wasting any more time responding to your comments. You should understand that it does not matter what people have done in the past if there is a better way to that task in the present. Moreover, there are no forces in GR/MGR; spacetime is curved and that governs how bodies move in spacetime. You shouldn't ask any question on forces depending on gravity until you understand GR and then MGR. I will not respond to you so go ahead and say anything you want.

Dear Gary Nash

Sorry, I haven’t follow the development of “Modified General Relativity and quantum theory in curved spacetime”. Actually, I never heard of the existence of the paper.

Anyway, time will tell although I foresee some difficulties. Because Einstein stated in 1920 that without matter there is no theory of General relativity while there is still a universe. And Eric Verlinde (2011) showed that Newtonian gravity is an emergent force field too. Thus I am afraid that we have to wait at least half a century before there is some consensus.

With kind regards, Sydney

Gary Nash ,

This discussion is not a good place for advertising your paper.

If you have so wonderful results, why cannot you start new discussion on your paper? Maybe some persons would be interested in it.

But this discussion on the physical quantity (the force) and not on the differential geometry

Dear Sydney, Einstein made that comment relative to his quest to unify gravity with electromagnetism. MGR and symmetrized QT satisfies that goal. Moreover, emergent gravity has an issue with the radial acceleration of galaxies; the Tully-Fisher relation in EG holds only for large radial distances - see "Testing Verlinde's Emergent gravity with the radial acceleration relation" Lelli, McGaugh and Schombert 2017. I think we are a little closer to understanding the Universe, but consensus is slow due to the enormous number of papers out there that nobody seems able to keep up with, including me for sure!

Gary

No it was 1920. Thus it has nothing to do with Einstein’s attempt to construct a unified field theory. The statement is part of his lectures about General relativity at Leiden University in the Netherlands. Anyway, I don’t think that I can contribute anything meaningful to this discussion at the moment.

With kind regards, Sydney

In 2014, Luc Blanchet published the paper "Gravitational radiation from Post-Newtonian Sources and Inspiring Compact Binary Systems" (Living Rev. Relativity, 17, (2014), 2). This is very detailed work, and formally Blanchet gives a solution for the radiation reaction of compact stars caused by gravitational radiation.

What is valuable in his work is that Blanchet gives a physical interpretation of his equations. But without taking into account one property of the radiation reaction force - what is its direction?

By analogy with classical electrodynamics, this force should be directed from the barycenter of the orbits. In classical electrodynamics, the problem of electron radiation in a hydrogen atom has not been solved. But in classical electrodynamics, the problem of radiation is removed by the introduction of quantum conditions. It is difficult to assume that gravitational radiation is a flow of gravity quanta.

Dear Vladimir Onoochin ,

the gravitational waves come out roughly from the barycenter of the binary.

Radiation reaction to the emission of the waves which have momentum and energy, is provided by the hypermedium, mathematically represented by the distorted Space-time.

Dear Stefano Quattrini ,

According to Wikipedia, the emission of the gravitational waves in binary system has been considered still by Peters and Mathews in 1963 - I cited his paper. Unitl now it is the basic work to calculate the parameters of the gravitational waves emitted by stars moving in the Keplerian orbits.

The authors use the results from the textbook of Landau-Lifshitz, 'Theory of field'. LL calculated these parameters in post-Newtonian approximation (expansion over small parameter 1/c). Then the problem is reduced to the problem of emission of some energy due to centrifugal acceleration of the massive body rotating in circular orbit.

In analogue with the action-reaction principle, if some body radiates, a back-reaction force should exist. Similar example exists in the electrodynamics. But since people couldn't resolve this problem - why a hydrogen atom does not collapse - Bohr introduced his postulates which correctness had been confirmed in 1920th.

However, the methods of the quantum mechanics are not applicable to the celesitial mechanics. So the back-reaction force should be described. Some authors accept an existence of this force. But - again - the problem is with a direction of this force.

Yes, it would be possible to assume that the rotating massive body deforms the space around itself. According to the GR such a deformation does not require the energy loss from the massive body. Therefore, if some part of deformation of the space leaves the massive body, it does not require the energy loss from this body. So the radiation of the gravitational waves should occur without the energy loss of the body.

Do you agree with my arguments? If not, please, say where I am wrong.

Dear Vladimir Onoochin ,

to my knowledge, understanding and opinion, the leading principle to follow is the conservation of energy and momentum in Physics and the second quantization which found the cut off energy denisty of vacuum is 10^110 joule/cm3....there is nothing else to resort to.

There is no energy loss relevant to the matter of the body itself, mass is an invariant in such case, assuming that during the falling/approaching there is no matter expulsion or transfer.

Said that, we have seriously to consider the role of the space around which is modeled as a sort of an hypermedium also by Maxwell.

The only way to explain consistently the mechanism of gravitation (and gravitational waves) is to assume that some energy, from such unknown background, is available and it is the reason for the kinetics of bodies.

Bodies are actually pushed together by this hypermedium (symmetric equivalent to a central force which makes the work to accelerate them), they increase their kinetic energy in their Center of mass system.

The reaction of the background to the unsteady motion of the bodies provokes gravitational waves in a similar way as what happens to a harmonic oscillator with a charge which sends emits EM waves.

The back reaction to the waves is provided by the Hypermedium which is quite likely equivalent to energy density of 10^110 joule/cm3, so it remains still whatever happens...

I have skimmed trough the discussion in this thread and it seems to me that everybody is considering "the energy loss in a system of binary stars" as a relativistic phenomenon. Is this so? I think that most astrophysics would point out that it is mostly a Newtonian phenomenon, due to tidal friction.

Dear Jose Gaite ,

to my opinion it is due to gravitational waves, this phenomenon can be also taken into account by a linearization of GR as shown by Hulse and Taylor in their Nobel lecture.

Dear Stefano,

I know Hulse-Taylor calculation, but it applies to compact objects, say neutron stars. In regular binaries, Newtonian effects can be more important. Presumably, an order-of-magnitude comparison is easy to work out, but I can't do it right now.

Dear Jose Gaite ,

I can understand that there are effects of such kind (tides) which could thermalize the kinetic energy of the stars....and for binary stars in general can be order of magnitudes larger than gravitational radiation, but to my understanding the question of Vladimir was focused on the gravitational radiation which Newtonian gravitation does cover.

Right Stefano. I have checked the formula for gravitational energy loss by radiation in an inspiral (per period) and it is proportional to the fifth power of the velocity, that is to say, negligible if it is not relativistic.