а болты я предлагаю делать деревянными, потому что интернет любую чухню стерпит.

VK: "So, about neutron stars I really do not know how to find words to defense such a concept."

What do you think about pulsars and the PSR 1913+16 discovery?

Relativistic mass isn't used much any more. In SR, it actually represents the total energy combining both mass and kinetic energy but it is pretty meaningless in GR.

The relativistic mass of a binary neutron star system is irrelevant to the question of whether they can merge. As they orbit each other their kinetic energy is gradually radiated away as (very weak) gravitational waves. This, of course, makes their orbit around each other smaller, reducing their potential energy and increasing their kinetic energy by the amount recently radiated away (half the lost potential energy replaces the kinetic energy already lost, and the other half increases the orbital kinetic energy of the stars, just as in the case of a ball falling toward the surface of the Earth). Once they get close enough to each other, tidal interactions can create a disk of gas of the plane of their orbit that frictionally depletes the kinetic energy even more, accelerating the decrease of the stars' orbital separation, and forcing them to "collide" and merge. Such collisions are incredibly violent, and produce two results. First, much of the material involved in the collision is blown into space, and becomes part of the interstellar medium. A substantial fraction of the elements heavier than iron is the result of such neutron-star collisions (theories of ordinary nuclear "burning" inside massive stars considerably underestimate the abundance of most of the very heavy elements, so although some of the gold, platinum and such in the Earth are atoms blown out by supernovae, most of the atoms of such elements are due to binary neutron star collisions). The sudden ejection of a large part of the mass-energy of the colliding stars, and (here's the second result) the probably common collapse of what remains of the stars into a stellar-mass black hole produces a sudden disruption of the space-time near the collision with enough energy to be detected by things such as LIGO at enormous distances, and the number of events of that sort so far detected, though small, is large enough that between all the binary neutron stars in all the galaxies in the observable universe, we can easily explain the excess abundance of very heavy elements.

On a completely different topic (but mentioned in an answer above, so worthy of mention here), black holes are not made of iron. "Normal" black holes created by iron-core collapse supernovae start off with a core of iron, but once the mass of that core exceeds the Chandrasekhar Limit for iron white dwarfs, all the electrons in the iron atoms are pushed into the protons, and the resulting nearly pure neutron fluid (which usually includes a substantial part of the star surrounding the iron core) collapses to a point of zero size and infinite density -- the singularity at the center of the black hole. That point is not made of anything, save pure mass-energy in a state of infinitely fluctuating transitions from energy to mass and back again. The rest of the black hole is simply very strongly curved essentially empty space-time, all the way out to interstellar space. At the point where the gravity is strong enough to keep anything including light from escaping we draw an imaginary boundary, the event horizon, that separates the interior of the black hole from the rest of the universe; but save when external material is falling into such an object, there is nothing either inside or outside the event horizon save for empty space, and the central singularity.

CS: As they orbit each other their kinetic energy is gradually radiated away as (very weak) gravitational waves. This, of course, makes their orbit around each other smaller, reducing their potential energy and increasing their kinetic energy by the amount recently radiated away (half the lost potential energy replaces the kinetic energy already lost, and the other half increases the orbital kinetic energy of the stars, just as in the case of a ball falling toward the surface of the Earth).

That is correct but might be hard for some to follow. As they spiral in, their speed increase as does the kinetic energy but the gravitational potential falls at twice the rate (see the Virial Theorem). Thus if the kinetic energy increases by E, the potential energy decreases by 2E, the total orbital energy decreases by E and that amount is radiated in the form of gravitational waves which LIGO can detect.

Once they get close enough, the rate of gravitational wave radiation is so high that they fall together in less than an orbit so there isn't much time for a disc to form. Some material will however be spun off by the "centrifugal force" as the objects fill their Roche lobes.

CS: First, much of the material involved in the collision is blown into space, and becomes part of the interstellar medium.

That depends on the masses, for GW170817 the sum of the progenitor masses was in the range 2.72 to 3.12 MSun (from 1.36+1.36 to 2.26+0.86). The ejecta totalled around 0.05 MSun and the radiated GW energy around 0.025 MSun which implies a remnant black hole of about 3 MSun. See:

https://arxiv.org/abs/1711.09638

https://www.ligo.caltech.edu/system/avm_image_sqls/binaries/99/original/GW170817_Factsheet.jpg?1508114118

CS: The sudden ejection of a large part of the mass-energy of the colliding stars, and (here's the second result) the probably common collapse of what remains of the stars into a stellar-mass black hole produces a sudden disruption of the space-time near the collision with enough energy to be detected by things such as LIGO ...

Actually, it is the steadily rising chirp that is the detectable aspect, the signal to noise ratio is much better when the signal can be integrated over thousands of cycles, the amplitude drops once the merger starts.

VK: I think nothing as I have never studied this object. However, the researchers ascribe to this object the availability of neutron stars. In my opinion, such stars cannot exist ...

Free neutrons are unstable and decay into a proton, an electron and an electron antineutrino.

https://en.wikipedia.org/wiki/Neutron#Free_neutron_decay

The inverse process is also possible and is called electron capture or sometimes inverse beta decay. The capture of an electron changes a nuclear proton to a neutron and emits an electron neutrino.

https://en.wikipedia.org/wiki/Electron_capture

Both processes have been well known in particle accelerators for a long time.

In the centre of very massive, burnt out stars which would be mainly iron or nickel, the loss of an electron reduces the volume required by an atom and if the pressure is high enough, the resulting reduction in gravitational binding energy can be large enough to make the transition more favourable than decay. It's a situation of dynamic equilibrium but for stars of sufficient mass, the core can become predominantly neutrons.

Evidence for their existence is varied but perhaps the simplest to follow is from millisecond pulsars, this is the fastest known for example:

https://en.wikipedia.org/wiki/PSR_J1748-2446ad

Its radius is less than 16 km and at its equator it is spinning at ~24% of the speed of light. Obviously the radius couldn't be more than ~65km or the surface would exceed the speed of light for the observed spin rate.

On the other hand, the densest normal stars are white dwarfs, and the most massive is RE J0317-853. It is the fastest known spinning white dwarf with a period of 725s:

http://adsabs.harvard.edu/abs/1998AAS...191.1511B

That spin rate is half a million time slower than PSR_J1748-2446ad.

Being supported by electron degeneracy, the radius of RE J0317-853 is comparable to the Earth:

http://scienceworld.wolfram.com/physics/WhiteDwarf.html

The existence of neutron stars is clearly not in doubt based simply on observation.

Hulse and Taylor observed this system:

https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary

Note the spin rate of the pulsar they measured is 17Hz or a period of 59ms. That is about 42 times slower than PSR_J1748-2446ad but still too fast for a white dwarf.

The gravitational waves of GW170817 rose to several kHz and the objects that merged had to have radii compatible with moving at less than the speed of light with a sub-millisecond orbital period. That works out at the same radius as is calculated for neutron stars.

VK: see also, e.g. http://www.rense.com/...

That's a notorious crackpot site.

VK: recoded by Dr. Pierre-Marie Robitaille

That guy believes in perpetual motion or perhaps doesn't understand that violating Kirchoff's Law also means violation of at least the second law of thermodynamics. Nothing from either of those sites is credible (and if you can't see their problems, it somewhat dents your own too).

VK: However, all the researchers point out that the reaction occurs only with the K-electron (the nearest to the nucleus), all other electrons in the atom studied remain at their initial positions.

The innermost electrons can be captured but once that happens, the others move in, about half way down the Wikipedia page you can see:

• Following capture of an inner electron from the atom, an outer electron replaces the electron that was captured and one or more characteristic X-ray photons is emitted in this process.

After that has happened, the new innermost electrons can be captured and so the process repeats. As I mentioned, it is a situation of dynamic equilibrium so the crust of the star has iron at the surface with layers of heavier elements beneath as the neutron fraction increases.

VK: If in fact neutron stars with the radius about several tens of km exists

Stars of that size certainly exist.

VK: their mergin cannot produce any other waves ...

The gravitational waves produced in GW170817 were observed for about 50 seconds, several thousand cycles at two cycles per orbit, before the merger event. Only the last few cycles relate to the merger, before that there is only a small tidal distortion of the bodies so the waves are almost indistinguishable from what they would be if you model the stars as simple point masses in a decaying mutual Keplerian orbit with negligible eccentricity. How what was observed would be modelled using your own ideas I couldn't say.

What I wrote is perfectly correct in this case Thierry. You need to remember that the inspiral reduces eccentricity to near zero so the bodies are moving in circular orbits at constant speed. The kinetic and potential energies are steadily changing as the total falls and as they do, the ratio remains constant.

More generally, the Virial Theorem deals with averages, Mathpages has a good derivation:

http://www.mathpages.com/home/kmath572/kmath572.htm

TDM: Take E = -2, and K = 2, then U = -4 ... Hence, the alleged virial theorem equation would give (according to you) 2K = - U, which is not correct.

It is correct.

TDM It is just a ordinary mathematical derivation ..

That is what physics is, the modelling of the real world using maths and nothing more.

TDM: doesn't even bother to give attention to Natural Philosophy.

Correct, it is pure physics.

TDM: While spiralling in, it is an illusion that the virial theorem would apply, because it is neither cyclic, nor infinitely lasting as a stable system

It doesn't need to be either, all that is required is that the time for the energy to be lost is much longer than the orbital period.

TDM: At each spiralling cycle, an error against 2K = - U is made, and this is cumulated all along the spiralling, causing a large error in the end.

Not at all, you haven't thought it through. Consider a planet that is moving too slowly for its radius (at aphelion), it will fall towards the Sun and speed up. Half an orbit later, it is much closer and moving faster, it is at perihelion. After another half orbit, it is back at aphelion bit a tiny bit closer due to the energy lost which means the potential energy has fallen, but because it didn't climb so far out, the velocity is a little higher too, so the error doesn't accumulate, it tends to decay.

In fact the higher speed at perihelion means there is a little more gravitational radiation so the speed is affected more and the eccentricity gets reduced, that's why the LIGO waveforms are expected to be those of circular orbits.

The rate of energy loss increases rapidly towards the end, and both tidal effects on the bodies and spin interactions become important so for the last dozen or so orbits, numerical modelling is required, but prior to that the Virial Theorem works just fine and what I said is entirely correct.

VK: You again talk about gravitational waves of general relativity produced in GW170817.

Just to clarify the terms, the name "GW170817" refers to the event where waves were detected.

VK: This object is very massive as the researchers who studied it claim.

It is not an object, it was the detection event. The source also was not an object, it was a binary star system, two separate neutron stars orbiting around each other.

VK: Let us assume that it might generate a gravitational wave of general relativity. But this wave can exist only in the framework of the metric of the GW170817.

Not true, there is only one metric which exists everywhere throughout the universe and the wave is a small perturbation of whatever it passes through.

VK: Between the object and the Earth we have a flat space, or flat metric.

No we don'twe have an FLRW background which is bent in some areas by galaxy clusters and on smaller scales by individual galaxies and stars. You might as well claim the skin of an an orange cannot have dimples because it is a perfect sphere.

VK: The solution of this gravitational wave cannot exist in flat metric.

Repeating statements that are patently untrue doesn't move the conversation forward at all Volodymyr, please open a textbook and correct your understanding.

VK: Nothing is found between the external and inner walls of the thermos

Right but geometry exists everywhere so there can never be any gap in the metric of GR, it exists throughout space and time and can be disturbed everywhere.

VK: Your LIGO interferometer could measure a bunch of inertons that from somewhere (maybe even from the Earth's crust)

We know LIGO measured something that was generated at a particular point in the sky and at a distance of 130 million light years because the waveform it measured told us where to look to find the kilonova. If you want to call that a bunch of "inertons", that's fine but the fact is they were generated far outside our galaxy.

VK: Regarding the capture of K-electron. Of course several electrons nearest to the nucleus can be captured. However, as I wrote already, a physical system of neutrons and protons exhibits instability at a certain ratio of neutrons to protons.

Normally yes but under extreme pressure, as I explained, fission into less massive atoms requires more space hence the material would have to expand raising the surface of the star. That means the lowest energy equilibrium state is displaced and nuclei with greater numbers of neutrons become favoured over smaller ones.

VK: this has never been observed as all chemical elements will be unstable by definition

Electron capture is observed, the Wikipedia article gives an example, hence the process is known to occur and the consequences are known.

VK: You wrote "the star has iron at the surface with layers of heavier elements beneath as the neutron fraction increases." This is a hypothesis!

Well obviously it's hard to verify! The first few elements can be predicted based on lab experiments beyond that it is quite uncertain and above 105 times the density of iron, a free 'gas' of neutrons can exist around the nuclei. There's no way to test that state of matter in the lab.

VK: You wrote that stars of small radius (tens of km only) certainly exist. I cannot say: "I believe this". I also cannot say: "I do not believe this".

The alternative is to believe that the surface of J1748-2446ad is moving faster than the speed of light. How fast can a sphere of liquid iron rotate before the surface is thrown off by centrifugal force? Try calculating the maximum radius for yourself, we know it rotates 716 times per second, I think you will get a few tens of km.

VK: 1) gravitational waves of general relativity - I already explained my position in previous comments

You did but what you said makes no sense because you imagine regions of space where there is no metric and those cannot exist, waves do pass through an otherwise flat metric just as capillary ripples can pass over a flat pond and simply claiming they don't with no basis is not a valid argument.

Your other two points are not relevant to this discussion, I disagree with them but let's not get sidetracked, the subject of Johan's question is GW170817.

VK: George Dishman, you do not possess the knowledge of submicroscopic physics, which was developed in my works.

It is true Volodymyr that I have not read your work but in this thread we are, as you note later, talking about a macroscopic effect, not microscopic. From my point of view, neither your comments nor other people's speculations on "gravitons" are relevant to the discussion.

VK: I do not know how "gravitational wave of general relativity" can move in principle because nobody in the word still does not describe this!

The textbooks do describe it so maybe you should read them before criticising. In fact there is more than one description an my own project, to which I intend to return and leave this thread shortly, is about comparing two complementary explanations.

VK: What is moving in "gravitational waves of general relativity" is impossible to described in any words - this is not mass at all, ...

What travels through space as light, known as photons, also has no mass.

VK: Whether it can influence a matter - none of theoretical works has been written so far!

Not true, it is in most good textbooks.

VK: For me it is really ridiculous what you are writing here...

For me it is ridiculous that you would criticise a theory that has been the only credible physical description of gravity for a century without first having read it.

VK: George, all the times you confuse concepts of quantum physics (quantum mechanics) and general relativity. General relativity is physical mathematics, or a kind of a pseudo-science, which can act only at a macroscopic scale. Quantum physics starts somewhere since 10 micrometers and spreads to smaller lengths.

Exactly, and gravitational waves are a macroscopic phenomenon on the scale of a binary star system so is best suited to a macroscopic analysis. From my point of view, you are the one confused.

VK: General relativity is acting at much larger scales, maybe above 1 m. However, let us assume general relativity also starts since 10 micrometers, however, this is the smallest size at which it still is correct.

No need, for GW170817 we can consider that nothing below 1km need be analysed at the source.

VK: Then if one needs an accuracy 10-21 in measuring the elongation (to catch gravitational waves of general relativity), the researcher must consider the behaviour of a ruler with the length about 1017 m.

No, you are neglecting the resolution of the measurement which depends on the wavelength of the laser light. The gravitational wave is macroscopic as we said above and even at frequencies of several kHz, the gravitational wavelength is of the order of 100km, the LIGO instrument can be considered to be fully immersed in the affected region.

For a Fabry-Perot design where the light can be passed along the arm say 2.5*102 times with an arm length of 4*103 m, the effective length is of the order of 106m. The laser runs at 1064nm or 10-6m so the ratio of the wavelength to the effective arm length is 10-12. An arm length variation of 10-23 will result in a variation of the optical output by 10-11 of a wavelength.

The circulating power in the cavity is of the order of 1MW or 106W so if the optics are arranged to give a first order output, a strain variation of 10-11 wavelengths will result in an optical output variation of 10-5W or 10μW which can be easily measured by a photodiode.

That is a very crude order-of-magnitude analysis but the conclusion is valid. The bottom line is that resolution is not the problem, seismic noise at low frequencies and photon shot noise at high frequencies are the limiting factors.

VK: only bla- bla-bla, which rather resembles the bleating of a ram, than science...).

You seem to be describing your own contribution only, or maybe your purpose has been to advertise your book.

"Relativistic mass doesn't exist, neither time dilation or length shrinking."

Dear Thierry,

thanks for your instructive comment. Time dilation and length shrinking may in fact be regarded as reciprocal phenomena. But isn't relativistic mass increase required for pushing kinetic energy of particles orbiting at close to luminal speed in a synchrotron accelerator? If so, what should we expect in case of inspiralling neutron stars?

VK: you again mix all together in one tangle. You wish to manipulate in terms of quantum physics applying its possibilities to measure something of a huge size.

No, that is what you are doing, trying to apply a microscopic model to explain macroscopic waves. I am saying that to understand LIGO, you should apply a purely classical analysis with no quantum aspects at all. For a basic understanding, quantisation is only evident as photon shot noise in the laser.

VK: If one cannot explain what exactly is irradiated, ..

I don't know what you mean by that, the whole universe is irradiated by the gravitational wave.

VK: You are talking about measuring a conventional wave, like an electromagnetic one, which is generated by atoms whose size is 10-10 m. However, the wave that you and your colleagues wished to measure has the other size of its node and antinode. The minimum size is 10-6 m.

Again your words are very muddled. The wavelength of the gravitational wave when it can first be detected is around 107m so the detector works best if it is smaller than that. On the other hand, the amplitude of the detected signal is proportional to the length of the arms so the larger the better. That creates the usual engineering compromise, there is an optimum size for detecting waves of a particular frequency and an arm length of a few km is quite good.

VK: This means that your detector must have a construction similar to a matrix in which the size of a cell is 10 micrometres. The appropriate cubic box includes about 1012 atoms. These atoms must act as a whole - they should be a preliminary cluster that catches a gravitational wave of general relativity. But from your explanation I can see that your interferometer does not have such a structure!

Then I have explained it well. Your understanding of the nature of what is being sought is badly flawed. The optical cavities are formed by a pair of mirrors, what is affected by the wave and is measured by the laser interferometer is the length of the gap between the mirrors or more accurately the time taken for the laser light to traverse the gap.

VK: In your comments you talk about individual atoms that receive signals

Nowhere did I say anything like that, perhaps you read someone else's comments and mistook them for mine.

VK: Regarding that double neutron star. Did those two stars already merge and the astronomers observe now only one neutron star?

LIGO received signals up to and including the merger but the frequency was several kHz at the end which put the signal into the shot noise range so the SNR at the merger was very poor.

.

The FERMI and INTEGRAL observatories saw a spike of gamma rays 1.7seconds after the two neutron stars first merged, what has been commonly known as a "short gamma ray burst" or SGRB for many years.

All the other observatories saw an expanding fireball as around 1% of the material was blown out by the explosion, that is called a "kilonova". I gave the details a few posts back, here's what I said:

• .. for GW170817 the sum of the progenitor masses was in the range 2.72 to 3.12 MSun (from 1.36+1.36 to 2.26+0.86). The ejecta totalled around 0.05 MSun and the radiated GW energy around 0.025 MSun which implies a remnant black hole of about 3 MSun. See:
• https://arxiv.org/abs/1711.09638
• https://www.ligo.caltech.edu/system/avm_image_sqls/binaries/99/original/GW170817_Factsheet.jpg?1508114118

VK: George, it seems to me you do not feel an actual conflict between quantum mechanics and general relativity. These two theories are in confrontation. One cannot use QM to prove something from GR.

While there are cases where they can be used together, in this case we agree. I am saying you need to use a classical analysis and stop trying to force your microscopic model onto large scale phenomena. That is what is creating the "muddle" to you talked about above.

Dear Volodymyr,

You wrote: “I think the term (gravitomagnetism) should be changed as magnetism does not present in phenomena of gravity.”

I agree. I think that the term “gravitational induction” (“g-induction”) is more suitable because the phenomenon to which the term refers is induced (produced) by the kinematics of a gravitating object.

(https://www.researchgate.net/publication/301891607_GRAVITO-ELECTROMAGNETISM_EXPLAINED_BY_THE_THEORY_OF_INFORMATONS-2)

Dear Thierry,

I refer to the induction as "gravitational induction" or "g-induction" (Bg) if its source is moving mass; and I use the term "electromagnetic induction" or "e-induction" (B) if its source is moving electric charge.

VK: George, thank you for the information on the fate of the neutron star discussed.

My pleasure Volodymyr, I am always happy to share sources.

VK: If gamma rays were observed, this means some electromagnetic process happened there in nucleus, ...

I believe the origin is primarily thermal radiation, a great deal of energy is released when two stars hit each other at around half the speed of light and the brief gamma radiation is simply due to the very high temperatures.

VK: which means that neutrons decay. So this is not a 100% pure neutron star.

As we have discussed, the neutron stars are probably mostly neutrons in the core but surrounded by outer layer of heavy elements.

The explosion ejects some of the matter and once the pressure is removed, the material breaks down into the heavy elements plus a cloud of free neutrons which then decay (with roughly 10 minutes half life) or are captured by other isotopes manufacturing more heavy elements.

VK: Regarding our discussion on gravitational waves of general relativity. This monster. It does not matter what is the length of the wave. The point is that this is an unusual wave. It does not influence individual atoms.

Correct.

VK: It has to involve groups of atoms, around 1012.

Wrong. Volodymyr, I have tried to explain this to you several times now but you seem to have a strange fixation on atoms and as a result you just ignore my words. I don't think I can make the operation of LIGO any clearer than what I said last time so if you can't understand this, it will be my last attempt.

GD: The optical cavities are formed by a pair of mirrors, what is affected by the gravitational wave and is measured by the laser interferometer is the length of the gap between the mirrors (or more accurately the time taken for the laser light to traverse the gap).

Dear Thierry,

You wrote: “How then would you call the induction that a variable magnetic field generates, which is then an electric field? Or the induction that a variable gyrotation field (= magnetic-like field of gravity) generates, which is then a gravitational field?”

In the context of your quote the term “electromagnetic induction” refers to an action: the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field. In the context of GEM, I use that term to refer to the physical quantity B, that characterizes the intensity of a magnetic field (the “flux density”). At first glance it would be more obvious to call B the “magnetic field” but that term is reserved for the vector H.

P.S. I think that this discussion doesn't fit with the subject of this treat. For that reason I placed a copy of this answer on https://www.researchgate.net/post/May_gravito-electromagnetism_be_an_alternative_to_Einsteins_theory_of_general_relativity, and if you wish to continue the discussion, I propose to do that there.

Dear Thierry, thanks a lot for inspiring aspects !!

Dear Johan

During the merge process, I do not have a definitive answer to your question. In the calculations involving neutron stars we have recently performed in our theoretical group, we have used a new approach for the nuclear relativistic effective quantum field theory with different degrees of freedom and also two different approaches in the general relativistic domain: we have used the field equations of the conventional general relativity and the pseudo-complex General Relativity (pc-GR) which have an extra term, of repulsive character, which may halt the gravitational attractive collapse of matter distributions in the evolution process of compact stars. This additional extra term simulates the presence of dark energy in the Universe. In this contribution we explored the presence of this additional term and we studied the role of dark energy in the structure of neutron stars composed by nucleons, hyperons, mesons, and weakly interacting massive fermion dark matter particles (WIMPs) held together by the presence of the nuclear force and the gravitational interaction superimposed to the repulsive background of dark energy. To describe the hadron-lepton sector we considered three different effective models for nuclear matter, Zimanyi-Moszkowski, Boguta-Bodmer, and the analytic parametrized coupling model, which we extended to consider, in the baryonic sector, the presence of the whole fundamental baryon octet. By solving the TOV equations we estimated the maximum gravitational mass of neutron stars. We got as the maximum mass of a neutron star 2.9 solar masses. My experience indicates however that you can have different values of the maximum mass of a neutron stars depending on the equation of state and thus to the composition, ingredients, and theoretical tools you use to make predictions about this topic. For instance, if you use the standard version of the Walecka model (QHD-I), you can reach 3.0 solar masses. The predictions are very model dependent.

Dear Cesar,

thanks for your elaborate comment on internal forces of neutron stars and corrections in view of dark energy. I should admit that my restricted theoretical background prevents me from estimating the work of your group in an adequate manner. My initial question was simply about whether or not relativistic mass increase of binary components, when orbiting each other with close to luminal speed, may have a significant influence on the final merging process. As I learn from Thierry De Mees, the concept of relativistic mass does not apply here in a way I previously suspected.

I think that several inconsistencies have emerged from LIGO project and the only net result will be to destroy what that project seems to defend: the set of relativity theories, starting from the general case.

I remind that:

• we have not a clear and unambiguously observation of neither a 'black hole' nor of a 'neutron star'
• LIGO 'observations' are far away from being without quotes

But I like watching the collapse of relativistic kingdom...

Dear Professor Vasconcellos,

Can you please explain for those of us less familiar with current NS knowledge how your work relates to that of Margalit and Metzger (other than the obvious inclusion of the dark energy component in your work):

Article Constraining the Maximum Mass of Neutron Stars From Multi-Me...

Dear Johan

Let me clarify one thing: what mass do you speak about? You're certainly referring to the mass of the neutron star, right? You are not you referring to the mass of its constituents, the protons, the neutrons, the hyperons, the leptons, the (virtual) mesons (they are relativistic)? But let me express that when you speak about the mass of the neutron star, there are two possible approaches to characterize the star mass: 1) the gravitational mass of a neutron star, given by the TOV equation, defined as a function of the internal density of the star; this mass is relativistic and is measured by using Keplers law when a satellite orbits the star; 2) the baryon mass of the star, given by the integral volume of the baryon number density times the baryon mass (also relativistic); this expression depends on the volume element of the Schwarzschild coordinates and the internal (relativistic) neutron star mass; the difference between these quantities corresponds to the binding energy of the star. This is why I am a bit confused by the claim that there would be no reliance on relativistic mass in the problem you place. The TOV equations correspond to a spherically symmetric solution of Einstein's relativistic equations. TOV: Tolman-Oppenheimer-Volkoff. And the mass of the constituents are also relativistic (special relativity domain). The dynamics of the mass merge process is more complex and is not considered in our calculations. What we calculate is the final result after the mass merge process when the neutron star then forms as the final stage of stellar evolution. There are two domains of calculations, one that involves the interaction between the internal stellar constituents (elementary particles), described in our case by nuclear relativistic field theories within the scope of special relativity. In this domain only nuclear, electromagnetic and weak interaction forces operate. And a second domain of calculation, in the scope of general relativity, where we carry the nuclear equation of state, obtained in the scope of special relativity, to the Einstein's equations of general relativity. It is in this second domain that gravitation comes into play, then shaping the mass of the neutron star. The nuclear state equation is the key to the definition of the final result.

Dear Thierry De Mees

Thank you for the message. It so happens that one could say, with propriety, that all theoretical predictions are model dependent. And it would be right. In the specific case I wanted to emphasize that small parameter entrances in determining the maximum mass of a neutron star can result in very different results. For example, a small modification of an essential parameter in the neutron star relativistic calculation, the nuclear binding energy, using for example the Walecka QHD-I model, may result in the addition (or decrease) of half solar mass in the final value of the mass of a neutron star.

VK: George, thank you for the information on the fate of the neutron star discussed.

Volodymyr, this paper is looking specifically at what the possible remnants might be and gives the inferred constraints based on the "multi-messenger" observations:

Article Constraining the Maximum Mass of Neutron Stars From Multi-Me...

https://arxiv.org/pdf/1710.05938

Dear Johan

Again I feel a bit confusing with your question: "My initial question was simply about whether or not relativistic mass increase of binary components, when orbiting each other with close to luminal speed, may have a significant influence on the final merging process." I do not know what you call a "process". My point is: all masses involved in the evolution process (supernova, accretion, merging, etc) ending in a compact stars (neutron star, dwarfs, black hole) must be described "in principle" by relativistic astrophysics physics. Your question has to do with results at the extreme relativistic domain compared to the relativistic domain? Is it your point. Because in my view there is no hypothesis to work in a classical domain at least as a guidence principle.

"I feel a bit confusing with your question"

Dear Cesar,

in a naive manner I simply thought of mass increase according to m = m0/(1 - v2/c2)1/2 when binary neutron star components move at orbiting velocities v close to c.

Well despite the elegancy of this formula this is not the answer. This formula relates the increase of the mass of a point particle as seen by a inertial observer relative to the proper referencial of the particle when the relative velocity of the two referencials increase. Your problem is much more complex. You cannot treat a neutron star as an elementary particle, without internal structure. And without rotational moment of inertia. And without the consequences of rotation in the mass configuration. 9The problem becomes much more complex if you wish to analyze the merger problem. You have to treat this problem in the realm of general relativity and the more simple description of the impact of the equation of state of each neutron star on the mass-radius relation is given by the TOV equations. Should moreover understand that as v -> c your equation becomes meaningless since m -> infinity...

"understand that as v -> c your equation becomes meaningless since m -> infinity..."

That's indeed what I was worrying about.

Besides Thierry and Volodymyr comments, keep in mind that all the relations involving the term 1-(v/c)^2 have not a catholic application, see next for more:

https://dx.doi.org/10.13140/RG.2.2.13329.6384

Dear Thierry

Gravity Probe B circled Earth from pole to pole for 17 months and used gyroscopes to measure two aspects of general relativity: the "geodetic effect," responsable for the predicted 2.8-centimeter decrement in its 40,000-kilometer orbit and the "frame-dragging effect", in which the rotation of the Earth twists the surrounding spacetime. And as a result the experiment confirmed the predictions of general relativity. My comment on the limit v -> c was related to a very important result of special relativity.

Dear Thierry

I can read and understand french. DeBroglie words about the difference between Lorentz-Fitzgerald and Lorentz contraction are very interesting. On the other hand, I am not familiar with the discovery of a second field of gravity by the experiment Gravity Probe b. What I know about is that Gravity Probe B circled Earth from pole to pole for 17 months starting 20 April 2004 and used gyroscopes to measure: 1. the spacetime dimple-like geodetic effect caused by the mass of the Earth; as a consequence of this effect the circumference of a circle around Earth becomes slightly shorter than the Euclidean value of 2π times the circle's radius. Gravity Probe B measured this way the predicted 2.8-centimeter decrement in the 40,000-kilometer orbit of the Earth to 0.25% precision. 2) the frame-dragging effect, in which the rrotation of the Earth twists the surrounding spacetime; this effect is less than 1/10 times as pronounced as the geodetic effect, to 19% precision. These results confirmed Einstein's predictions of GR and are not related to magnetic interactions. They are geometric topological gravitational effects related to the presence of mass.

Dear Thierry

please take a look on the material below:

(http://iopscience.iop.org/journal/0264-9381/page/Focus-issue-on-Gravity-Probe-B)

Focus issue: Gravity Probe B

📷 The Gravity Probe B experiment was carried out in collaboration between Stanford University, NASA, Lockheed Martin and KACST.

Guest editors

C W F Everitt B Muhlfelder C M Will A S Silbergleit

On 4 May 2011, NASA announced the long-awaited results of Gravity Probe B (GP-B) [1], and a month later the results appeared in Phys. Rev. Lett. [2]. After more than 47 years and 750 million dollars, GP-B had succeeded in measuring the general relativistic geodetic and frame-dragging effects on orbiting gyroscopes. In this focus issue, CQGpublishes a set of refereed papers that provide the complete details of the experiment, from design of the spacecraft to the final data analysis, thus bringing to a close an extraordinary chapter in experimental gravitation.

According to Einstein's theory, a massive, rotating body such as the Earth both warps spacetime and drags spacetime a tiny bit around with it, and these effects are what the four gyroscopes aboard the Earth-orbiting GP-B satellite were designed to measure. The satellite followed a polar orbit about 640 km above the Earth's surface. For such an orbit, the geodetic precession, a combination of space curvature and Thomas precession, amounts to about 6.6 arcseconds per year in the plane of the orbit, or in a North–South direction. The 'frame-dragging' effect, caused by the Earth's rotation, amounts to about 39 milliarcseconds per year, perpendicular to the orbital plane, or in the East–West direction.

Each gyroscope was a fused silica rotor, about the size of a ping-pong ball, machined to be spherical and homogeneous to tolerances better than a part per million, and coated with a thin film of niobium. The gyroscope assembly sat in a dewar of 2440 l of liquid helium, held at 1.8° Kelvin. At this temperature, niobium is a superconductor, and the supercurrents in the niobium of each spinning rotor produce a 'London magnetic moment' parallel to its spin axis. Extremely sensitive magnetometers (superconducting quantum interference devices, or SQUIDs) attached to the cavities housing the gyroscopes measured the minute changes in the orientation of the gyros' magnetic moments.

At the start of the mission, the four gyros were aligned to spin along the symmetry axis of the spacecraft. This coincided with the optical axis of a telescope directly mounted on the end of the structure housing the rotors. Spacecraft thrusters oriented the telescope to point precisely toward the star IM Pegasi (HR 8703) in our galaxy (except when the Earth intervened, once per orbit). In order to average out numerous unwanted torques on the rotors, the spacecraft rotated about its axis once every 78 s.

GP-B started in late 1963 when NASA funded the initial R&D work that identified the new technologies needed to make such a difficult measurement possible. In 1981, Francis Everitt became principal investigator of GP-B, and the project moved to the mission design phase in 1984. Initial plans called for a test of some of the key technologies in a space shuttle flight (similar in intent to the LISA Pathfinder mission) followed by a launch of the full experiment from the Shuttle, but the 1986 Challenger disaster ended that plan and forced a redesign of the mission for launch on a Delta rocket without a technology demonstration precursor. Following a major review of the program by a US National Academy of Sciences committee in 1994, GP-B was approved for full flight development, and began to collaborate with Lockheed–Martin and Marshall Space Flight Center. The satellite launched on 20 April 2004 for a 16 month mission, but another five years of data analysis following the mission were needed to tease out the effects of relativity from a background of other disturbances.

Almost every aspect of the spacecraft, its subsystems, and the science instrumentation performed extremely well, some far better than expected. Still, the success of such a complex and delicate experiment boils down to figuring out the sources of error. Unfortunately, three important, but unexpected, phenomena were discovered during the experiment that affected the accuracy of the results.

First, because each rotor is not exactly spherical, its principal axis should rotate around its spin axis with a period of several hours, with a fixed angle between the two axes. This is the familiar 'polhode' motion of a spinning top. This behavior was expected and was an essential tool for calibrating the SQUID output. What was unexpected was an observed decrease with time of the polhode period and angle of each rotor, implying the presence of some damping mechanism. In addition, each rotor was found to make occasional, seemingly random 'jumps' in its orientation—some as large as 100 milliarcseconds. Some rotors displayed more frequent jumps than others. Finally, during a planned 40-day, end-of-mission calibration phase, the team discovered that when the spacecraft was deliberately pointed away from the guide star by a large angle, the misalignments between the rotors and their housings induced much larger torques on the rotors than expected. From this, they inferred that even the very small misalignments that occurred routinely during the science phase of the mission were inducing torques that were probably several hundred times larger than anticipated.

What ensued during the data analysis phase was worthy of a detective novel. The culprit was the 'patch effect', a well-known phenomenon in superconductivity.

Careful examination of the full panoply of data taken both during the mission and during the post-mission phase revealed that interactions between random patches of electrostatic potential fixed to the surface of each rotor and similar patches on the inner surface of its spherical chamber were causing the extraneous torques. In principle, the rolling spacecraft should have suppressed these effects, but they were larger than expected from tests done prior to launch. Fortunately, such patches are fixed on superconducting surfaces, and so it was possible to build a parametrized model of the patches on both surfaces using multipole expansions, and to calculate the torques induced by those interactions when the spin and spacecraft axes are misaligned, as a function of the parameters. The model correctly accounted for all the anomalies seen, including the 'jumps'.

The original goal of GP-B was to measure the frame-dragging precession with an accuracy of 1%, but the discovery of the anomalous torques made this impossible. Although the GP-B team were able to model the effects of the patches, they had to pay the price of the increase in error that comes from using a model with so many parameters. The experiment uncertainty quoted in the final result—roughly 20% for frame dragging—is almost totally dominated by those errors. Nevertheless, after the model was applied to each rotor, all four gyros showed consistent relativistic precessions.

When GP-B was first conceived in the early 1960s, tests of general relativity were few and far between, and most were of limited precision. But during the ensuing decades, researchers made enormous progress in experimental gravity, performing tests of the theory by studying the solar system and binary pulsars [3]. Already by the middle 1970s, some argued that the so-called parametrized post-Newtonian (PPN) parameters that characterize metric theories of gravity were already known to better accuracy than GP-B could ever achieve [4]. Given its projected high cost, critics argued for the cancellation of the GP-B mission. The counter-argument was that all such assertions involved theoretical assumptions about the class of theories encompassed by the PPN approach, and that all existing bounds on the PPN parameters involved phenomena entirely different from the precession of a gyroscope. All these issues were debated, for example, in the 1994 review of GP-B that recommended its completion.

The most serious competition for the results from GP-B comes from the LAGEOS experiment, in which lasers accurately track the paths of two satellites orbiting the Earth, both optimized for laser tracking. Relativistic frame dragging induces a small precession (around 30 milliarcseconds per year) of the orbital plane of each satellite in the direction of the Earth's rotation. However, the competing Newtonian effect of the Earth's nonspherical shape has to be subtracted to extremely high precision using a model of the Earth's gravity field. The first published result from LAGEOS in 1998 quoted an error for frame-dragging of 20%–30%, though this result was somewhat optimistic given the quality of the gravity models available at the time. Later, the GRACE geodesy mission offered dramatically improved Earth gravity models, and the analysis of the LAGEOS satellites finally yielded tests at a quoted level of approximately 10% [5]. A third satellite called LARES was launched in 2012, with the goal of ultimately providing a test of frame dragging at the 1% level.

In 1997, soon after the transition of GP-B to a full-fledged flight program, NASA asked Clifford Will to establish and Chair an external Science Advisory Committee (SAC), whose charge was to give independent advice to both GP-B and NASA in order to ensure that, whatever science came out of such a complex project, it would be credible, defensible and transparent. The committee consisted of David Bartlett (University of Colorado), Robert Reasenberg (Harvard CFA), Robert Richardson (Cornell), John Ries (University of Texas), Peter Saulson (Syracuse) and Edward (Ned) Wright (UCLA). During the course of 20 meetings from 1998 to 2011 the SAC reviewed and monitored every detail of the experimental fight development, mission operations, and data analysis. CQG is grateful to members of the SAC, along with numerous other reviewers, for serving as referees for the papers in this issue.

The issue begins with an overarching science paper that summarizes the mission and the data analysis. It also includes three papers detailing the data analysis and a paper providing some theoretical context. The remaining papers are primarily technological, describing everything from how the rotors were made and tested to the drag-free control of the spacecraft. In addition to these published papers, it is useful to point out that, as a matter of NASA policy for all space missions, the data from GP-B is publicly available.

Acknowledgements

We are grateful to American Physical Society for permission to incorporate material from Physics 4, 43 (2011) (http://physics.aps.org/articles/v4/43) into this preface.

References

[1] Press conference available at (http://www.youtube.com/watch?v=SBiY0Fn1ze4)

[2] Everitt C W F et al 2011 Phys. Rev. Lett. 106 221101

[3] Will C M 1993 Was Einstein Right? (NY: Basic Books, Perseus)

[4] Will C M 2014 Living Rev. Relativ. 17 4

[5] Ciufolini I et al 2010 General Relativity and John Archibald Wheeler ed I Ciufolini and R A Matzner (Dordrecht: Springer) 371 p

"Although the GP-B team were able to model the effects of the patches, they had to pay the price of the increase in error that comes from using a model with so many parameters. The experiment uncertainty quoted in the final result—roughly 20% for frame dragging—is almost totally dominated by those errors. Nevertheless, after the model was applied to each rotor, all four gyros showed consistent relativistic precessions."

From my view as an independent experimental physicist the "consistent relativistic precessions" have been achieved by adaptation of questionable data according to expectations.

Thierry, I just found that gravitomagnetism predicts half of the GR value:

https://en.wikipedia.org/wiki/Gravitoelectromagnetism#Gravitomagnetic_fields_of_astronomical_objects

The GR prediction for that effect for Gravity Probe B was 39.2mas/year so the GM prediction would be 19.6mas/year. The measured value was 37.2±7.2 so experimentally the GM prediction is off by 2.4 sigma while GR is within 0.3 sigma, GR is 8 times more accurate than GM. I recently posted that in the following thread so can we try to keep it to one of them:

https://www.researchgate.net/post/Shapiro_delay_slowing_of_c_or_path_increase

Hi Joahn

returning to your original question, I presume you are interested in the merger of binary neutron star (BNS) systems which are predicted to be progenitors of short gamma-ray bursts (GRBs). I just mention that a recent probe of this association came with the recent detection of gravitational waves (GWs) from a BNS merger by Advanced LIGO and Advanced Virgo (GW170817), in coincidence with the short GRB 170817A observed by Fermi-GBM and INTEGRAL. See https://arxiv.org/pdf/1801.05167.pdf

Now concerning the mass of a neutron star, as a theoretician, my experience comes from calculation of equations of state of neutron stars, pulsars and strange and quark stars, using relativistic nuclear effective theory and the tools of General Relativity. More precisle, the Tolman-Oppenheimer-Volkoff equations and nuclear effective relativistic theory. Using a formalism with many-body nuclear forces, I got around 2.2 - 2.5 solar masses. The present experimental knowledge of the mass of neutron stars is limited to around 2.17solar mass. see for instance:

Constraining the Maximum Mass of Neutron Stars From Multi-Messenger Observations of GW170817

Ben Margalit, Brian Metzger(Submitted on 16 Oct 2017 (v1), last revised 8 Nov 2017 (this version, v2))

We combine electromagnetic (EM) and gravitational wave (GW) information on the binary neutron star (NS) merger GW170817 in order to constrain the radii Rnsand maximum mass Mmax of NSs. GW170817 was followed by a range of EM counterparts, including a weak gamma-ray burst (GRB), kilonova (KN) emission from the radioactive decay of the merger ejecta, and X-ray/radio emission consistent with being the synchrotron afterglow of a more powerful off-axis jet. The type of compact remnant produced in the immediate merger aftermath, and its predicted EM signal, depend sensitively on the high-density NS equation of state (EOS). For a soft EOS which supports a low Mmax, the merger undergoes a prompt collapse accompanied by a small quantity of shock-heated or disk wind ejecta, inconsistent with the large quantity ≳10−2M⊙ of lanthanide-free ejecta inferred from the KN. On the other hand, if Mmax is sufficiently large, then the merger product is a rapidly-rotating supramassive NS (SMNS), which must spin-down before collapsing into a black hole. A fraction of the enormous rotational energy necessarily released by the SMNS during this process is transferred to the ejecta, either into the GRB jet (energy EGRB) or the KN ejecta (energy Eej), also inconsistent with observations. By combining the total binary mass of GW170817 inferred from the GW signal with conservative upper limits on EGRB and Eejfrom EM observations, we constrain the likelihood probability of a wide-range of previously-allowed EOS. These two constraints delineate an allowed region of the Mmax−Rns parameter space, which once marginalized over NS radius places an upper limit of Mmax≲2.17M⊙ (90\%), which is tighter or arguably less model-dependent than other current constraints.

I recently found this although it has been around for some time. It incorporates quantum vacuum polarization into the TOV limit:

Article Stellar Equilibrium in Semiclassical Gravity

Dear George

I downloaded the article. I found very interesting the contents of the TOV equations. I did not understand up to now what are the values of the parametrizations the authors use to describe quantum vacuum polarization.

Regarding your statement, "From the signal frequency received by LIGO gravitational wave antennas that is interpreted as originating from a binary neutron star system, we calculate orbital speed of merging components at close to luminal speed c". In the following draft of my paper, it is shown gravitational waves go faster than gamma rays, while both gravitational and gamma rays go at superluminal velocities.

Discovery Of 235-uranium Fission Taking Place In Collision Of Neutron Stars Cause Gravitational Waves And Electromagnetic Radiations

• March 2018
• 📷Padmanabha Rao

  Article Named ‘Neutron Stars’ but failed to understand as 235^Uraniu...

Hi,

The most recent merging of two neutron stars spiraling into each other (August 2017) produced gravitational-waves which allowed physicists to calculate their combined mass to be 2.73 solar masses. And two seconds after the production of gravitational waves, orbiting telescopes detected a powerful, short gamma ray burst. The neutron star created in a merger was traced as it lost its fast-spinning outer layers, spun as a rigid body, then collapsed into a black hole. That allowed researchers to infer the maximum mass of a stable neutron star.  (around 2.2 solar masses is our present understanding).

Indeed it was GW170817! 2.73 Solar masses.

In fact, the observation of the Gravitational Waves from the binary neutron star coalescence, GW170817allowed the scientists to explore the equation of state of neutron stars at super-nuclear densities. The coalescence is encoded as a change in gravitational-wave phase evolution caused by the tidal deformation of the neutron stars. The "knowledge" of the equation of state allows scientists, by combining this information with the Tolman-Oppenheimer-Volkoff equations of general relativity to obtain the maximum mass of the merger. They got 2.37 solar masses and a maximum mass fro neutron stars of 2.2 solar masses. At leading order, the tidal effects are imprinted in the gravitational-wave signal through the binary tidal deformability which affects in a "controlled" way the different models of equations of state for dense nuclear matter.