Hi John

Excellent question, 

Ii is possible that  the black holes have some internal structure with a core at the center, and at some point the two "cores" merge and become one object, hence stop generating any self rotational (in-spiraling) gravitational waves. That core (in small black holes) is predicted to be 1/9 the Schwarzschild radius 

The bifurcation is particularly interesting as it experimentally confirms this observation, as the ratio of the peak and trough frequencies of the up and down chirps is  9.

There are a lot of problems with GTR, not least is presents with infinite singularities, does not explain dark matter, it cannot fully explain dark energy and gives us infinite time dilation at the event horizon, which means that matter cannot enter the black hole in the lifetime of the Universe

Herein some peer reviewed international publications that resolve this.

1).First to obviate the infinite density singularities.

1a)https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the galaxy.

2a)https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the galactic halo.

3a)https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter.

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation damping ) and is corroborated by black hole studies.

5a)https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

7). It does not offer infinite time dilation at the event horizon,

https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg

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Article An advanced modification of dynamic gravitation

Article An advanced dynamic adaptation of Newtonian equations of gravity

Article String quintessence and the formulation of advanced quantum gravity

Article Advances in Black Hole Gravitational Physics and Cold Dark M...

Article Corroboration of Dynamic Black Hole Gravitational Physics fr...

Article The formulation of Dynamic Newtonian advanced gravity, DNAg

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

Article Finite Gravitational Time Dilation In Black Holes Using Dyna...

"at some point the two "cores" merge and become one object, hence stop generating any self rotational (in-spiraling) gravitational waves."

Andrew,

thanks for your comment. Unfortunately, I'm not able to respond in an adequate manner as I'm not familiar with the theoretical background. But maybe you can give some short comment on why "disappearance" of several solar masses, as apparently expected in case of a BBH merger, won't have any noticeable effect on spacetime dynamics when inspiraling motion of binaries before and ringdown after merge are expected to send out clear GW signals. I would expect an accompanying energy burst comparable to what happens in case of a supernova explosion.

Well the standard answer would be that we are shielded by the event horizon. In standard BH physics nothing can exit the event horizon because nothing can exceed the speed of light, and there is an infinite force an no time passes at the event horizon.

As it happens that is only partly true, but the gravitational field strength  does rise exponentially inside the black hole. Which is why you see a rapid up chirp in the GWs.

You also see a down chirp, at the same time which decreases in strength and frequency (see attached).

The energy release by the merger is not in the form of matter as no matter can exceed the speed of light. It is in the form of GW release. This is the release of gravitons.

Now the question remains how does gravity escape a black hole (The presence of GWs means that gravity is not an emergent force).

That gravity escapes a black hole strongly implies that gravitons can be tachyonic i.e faster than the speed of light, (although their average speed is clearly the speed of light), and that explains the up chirp and down chirp seen in all the BH mergers so far and a difference in frequency.

Suffice it to say that that tachyonic gravitons do not experience a gravitational redshift

"a considerable quantity of matter spiralled away from the binary system at the height of the merger"

Andrew,

that's what I just read in the abstract of your above mentioned paper. So you think no mass at all will be converted into energy? My impression is that black hole features are still discussed with some reservation, a lot of theoretical speculation, indeed, derived from rather poor experimental findings, while we still cannot be sure signals result from local instrumental rather than from remote cosmic events.

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

Instead of working for an alleged source of 1.3 billion light years away, we could just examine the Milky Way supposed 'BH' which is just 25000 light years. So, what about that closer to us 'object'?

Yet lots of mass converted into energy in the form of gravitons to produce GWs

"mass converted into energy in the form of gravitons"

So in fact we not only have a two-fold but rather a multifold discovery: (1) gravitational waves, (2) black holes, (3) black-hole mergers, (4) gravitons. Congratulations, surely deserves four Nobel awards!

JKF: But maybe you can give some short comment on why "disappearance" of several solar masses, as apparently expected in case of a BBH merger, won't have any noticeable effect on spacetime dynamics when inspiraling motion of binaries before and ringdown after merge are expected to send out clear GW signals.

You seem to be under the impression that the loss of 3 solar masses occurs at the time of merger, that is not the case. That amount of energy is the total integrated over the inspiral and merger, the amount in the last few cycles is only a small part of it.

AW: The energy release by the merger is not in the form of matter as no matter can exceed the speed of light. It is in the form of GW release.

That is correct, I've explained that to Johan several times.

AW: This is the release of gravitons.

Gravitons are purely hypothetical at present, gravitational wave analysis is currently purely classical.

AW: Now the question remains how does gravity escape a black hole

The waves do not need to escape from either BH, they are formed by the rotation of the system as a whole so are created well outside the event horizons.

DC: Instead of working for an alleged source of 1.3 billion light years away, we could just examine the Milky Way supposed 'BH' which is just 25000 light years. So, what about that closer to us 'object'?

It is not a binary system so does not create any gravitational waves.

"That amount of energy is the total integrated over the inspiral and merger"

Thanks, George, for the enlightenment.

"The waves do not need to escape from either BH, they are formed by the rotation of the system as a whole so are created well outside the event horizons"

Does this apply for the ringdown phase as well in view of expanded event horizon after merge?

The waves from the ringdown phase are from distortions in the shape of the horizon as I understand it. The "no hair" theorem says the eventual equilibrium shape is defined by a few parameters and any deviation from that produces waves that have a "backreaction" that smoothes out the horizon.

Caution Johan

Not sure that convention has the full picture under GTR. You see mathematically most the energy must  be expended after the event horizons' are crossed.

Logically gravitation must be able to cross the event horizon or there can be no gravitational effects beyond the event horizon.

P.S.  "No Hair theorem" has little substance. You can thank me later for this insight.

AW: Not sure that convention has the full picture under GTR. You see mathematically most the energy must  be expended after the event horizons' are crossed.

Andrew, you only have to look at the waveform to see that's not true.

How so, George. If gravitation crosses the event horizon which it logically should do then the corollary  is that more energy would come from inside the black hole event horizon as the strength of gravity becomes greater, hence exactly the bifurcation we see in the waveform.

AW: How so, George.

In an AC electrical waveform, as I'm sure you know, the power is proportional to the square of the voltage and the energy in a half cycle is the integral of the power over that period.

In gravitational waves, the power is proportional to the square of the strain, and strain is the waveform that LIGO measures. If you integrate the square of the area under the curve, you get an indication of the energy. The inspiral lasts many cycles, the ringdown just a couple at rapidly decreasing amplitude.

AW: If gravitation crosses the event horizon which it logically should do then the corollary is that more energy would come from inside the black hole event horizon ..

If any form of energy could come from inside, it wouldn't be an event horizon!

Gravitational waves are produced by the binary system, not the individual bodies. The waves aren't even formed until around a wavelength away from the system which is several times larger than the event horizon. For binary neutron star mergers which they also hope to see, there are no event horizons (unless the merger produces a new black hole, but that remains to be seen, or not).

GD: "That amount of energy is the total integrated over the inspiral and merger"

What is the mechanism of energy conversion from mass into spacetime distortion?

I believe it is called "backreaction" but that's just a general term (Sabine Hossenfelder use it for the title of her blog which is quite well known).

A Newtonian analogy might be that the energy released comes from the increasingly negative gravitational potential but really you'd have to look into GR in some detail to get a meaningful answer.

P.S. Thinking a bit more about the question, if the radius of the orbit reduces , we would expect the speed to increase as it does in an elliptical orbit. The backreaction must act to reduce the speed like a drag term, essentially a recoil from launching the waves. That means the waves energy directly comes from the kinetic energy of the orbiting bodies. It is the mass of the system that is reduced, not the mass of the components.

GD: "I believe it is called "backreaction" but that's just a general term ... you'd have to look into GR in some detail to get a meaningful answer."

So we don't really know how it works, but we do know that it must work in order to support our claims?

JKF: So we don't really know how it works

That depends on who you are including in "we".

Those who have studied GR to a level of detail well beyond my own understanding do know how it works, personally I don't, but I'm just an amateur studying this as a hobby.

I do know that gravitational waves carry momentum so if the orbiting bodies emit waves, there must be a recoil force which would slow the orbital velocity, or at least prevent it increasing as fast as would expect for a stable Keplerian orbit, thus allowing the radius to decrease.

Are you familiar with the application of the Virial Theorem to Keplerian orbits? I'm assuming you are.

"The waves from the ringdown phase are from distortions in the shape of the horizon as I understand it."

George,

According to my understanding, a stellar object at the end of its life may collapse into a neutron star. When the object exceds a few solar masses then the Schwarzschildradius is larger than the object radius, so it will become invisible as it is "hidden" inside its "event horizon", and the object is termed a "black hole".

When the supposed components of a binary black hole system as associated with claimed discovery of gravitational waves are "hidden" neutron stars as described above, and the mass of the binary system after merge is of the order 60 solar masses, then the respective neutron stars after merge of their event horizons are still quite distant from each other as measured in units of their "real" neutron star diameter. Consequently, inspiral motion should be expected to continue inside the joint event horizon with two well separated objects quite a number of turns before they will get into contact. Shouldn't we expect still increasing signal amplitudes and frequencies from inspiral motion after merge of event horizons and an outstanding signal in case of a "bodily" merging event?

"there must be a recoil force which would slow the orbital velocity"

Yes, of course, and I expect GW radiation power will correspond to loss of orbital kinetic energy such as known from PSR1913+16 binary neutron star system. But where does dissipation of mass come into play?

Johan, it will be easier if I answer your second question first but I need to know as I asked before, are you familiar with the Virial Theorem and Keplerian orbits?

"are you familiar with the Virial Theorem and Keplerian orbits?"

Not yet.

OK, have a look at "The simplest example" in the first link and a similar summary in the second. There's a much more rigorous derivation in the third. The fourth gives the same formula but relates it to heat. The fifth link shows how it can be used to find the mass of astronomical groupings. This was how Zwicky first discovered dark matter back in the 1930's (last link).

The relevance is that the mass of a binary system measured from far away is given by:

Msys = Esys / c2

The total energy of the system is the sum of the masses of the two bodies plus the "orbital energy" which is the sum of the potential and kinetic. Normally the sum of the PE and KE averaged over an orbit is constant and complies with the Virial Theorem in a Keplerian orbit, although energy can shift between PE and KE in an elliptical orbit.

If kinetic energy is lost due to the recoil as GW are radiated, the total orbital energy falls while the Virial Theorem keeps the ratio constan. Since the PE becomes more negative at twice the rate that the KE becomes more positive, the speed actually increases although the total energy decreases.

Since the apparent mass of the system comes from both the objects and the orbital energy, it also falls as the GW carry away energy.

http://math.ucr.edu/home/baez/virial.html

http://www.astro.cornell.edu/academics/courses/astro201/vt.htm

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

http://sgoodwin.staff.shef.ac.uk/virial.pdf

http://astronomy.swin.edu.au/cosmos/V/Virial+Theorem

https://en.wikipedia.org/wiki/Fritz_Zwicky#Dark_matter

Thanks, George, for instructive links. In fact, I'm doubtful of dark matter as deduced, in particular, by Zwicky from the "Virial Theorem" in view of annexed paper.  

"the speed actually increases although the total energy decreases."

I'm quite familiar with this phenomenon in view of planetary motion without referring to the Virial Theorem.

"Since the apparent mass of the system comes from both the objects and the orbital energy, it also falls as the GW carry away energy"

Yes, of course, but I understand GW energy is fed from orbital part of Esys as according to PSR1913+16 observation.

http://gsjournal.net/Science-Journals/Research%20Papers-Gravity/Download/6955

OK, so the mass of the system as measured by a distant observer falls as the GW energy is radiated away reducing the orbital energy. You seem to know that already because you said:

JKF: Yes, of course, and I expect GW radiation power will correspond to loss of orbital kinetic energy such as known from PSR1913+16 binary neutron star system.

You asked:

JKF: But where does dissipation of mass come into play?

I'm sure you are aware of "E=mc2" so as the orbital energy is radiated away, the system mass is reduced accordingly so I don't understand what you are asking Johan. 

The total energy of the system is the sum of the masses of the two bodies plus the "orbital energy"

That's what you stated before, and I don't see any reason to doubt that GW power is fed only from the "orbital energy" part of Esys. By "dissipation of mass" I in fact refer to the "material" part of Esys.

The "material" part doesn't change, although that word is not very applicable to black holes. The mass of the Earth is less than the sum of the mass of the atoms that constitute it for example because the total mass includes the negative binding energy. The same would be true for other merged objects, we just change the name because the parts are no longer orbiting but are bound.

GW: "the total mass includes the negative binding energy."

Do you think loss of ~ 3 solar masses is equivalent to negative binding energy of black hole merger with cumulative ~ 60 solar masses, and equivalent energy is dissipated during inspiral phase via gravitational wave "radiation"?

That's correct. If the system wasn't able to get rid of the orbital energy, they would not have merged because the orbit would be stable.

"That's correct."

I'm not shure about that: ~ 5% binding energy with respect to total mass appears rather large in view of ~ 0.9% maximum in case of atomic nuclei around iron with clearly decreasing tendency towards heavier nuclei.

JKF: ~5% binding energy with respect to total mass appears rather large in view of ~0.9% maximum in case of atomic nuclei around iron

Nuclear burning is much less efficient than gravitational energy release, hydrogen to helium is only around 0.7% which is most of the binding energy in iron as you note.

Theory says the maximum for simple material falling into a non-rotating hole is 1-√(8/9) which is about 5.72% but the likelihood is that both holes are rotating so I might have expected a higher value. It depends on the relationship between the spin axes in some complex manner though so intuition isn't much of a guide.

Accretion onto a solid surface like a neutron star can release more than 30% and for a perfect accretion disc around a black hole, matter falling to the innermost stable orbit can in theory release up to 42%! That's what powers quasars. Various factors reduce that in practice but astronomers use a rough guide of about 10% as representative of real world emission efficiency.

Thanks, George, for instructive data.

No problem Johan. Much of this stuff is available on-line in lecture notes but it isn't easy to find unless you know what to look for. Back on page 2, you also commented about the nature of a black hole and I said I'd answer your second question first. I think we've done that so I'll address the other comment:

JKF: According to my understanding, a stellar object at the end of its life may collapse into a neutron star. When the object exceeds a few solar masses then the Schwarzschild radius is larger than the object radius, so it will become invisible as it is "hidden" inside its "event horizon", and the object is termed a "black hole".

Some will end as neutron stars as the result of a supernova, less massive stars can end as white dwarfs. Adding material to a neutron star, for example from a normal companion star in a binary system, is one way to create a black hole and a good way to investigate their nature. The first link is a presentation from 2009 that gives an overview of the subject. The key to understanding what happens are the mass/radius charts on page 3/5 and the last page. The second link is a more recent summary (2016) but with a lot more detail. However, the same style of diagram is shown in Figure 7 (attached).

If you imagine pouring more rock onto the Moon, the more you add, the larger it would get. Try the with a neutron star and an odd thing happens, as you add more mass, the radius decreases. That is because the added weight compresses the core more than the surface grows. What happens at some point is that the situation becomes unstable, the radius falls which increases the surface gravity which compresses the core more which then shrinks ever faster. At somewhere just above 2 Solar masses (that's the largest neutron stars known), the neutron material or whatever weird stuff is in the core can no longer produce a high enough pressure to stop the neutron star imploding. The radius then drops below the Schwarzschild radius for that mass and continues to fall to near zero according to classical GR. The reason for that is that remaining at a fixed radius would require the surface to exceed the speed of light relative to a freely falling particle which as far as we know is impossible.

What happens in reality cannot be predicted without a quantum gravity theory but that may only come into play at sub-atomic scales.

https://constellation.gsfc.nasa.gov/resources/presentations/PDFs/NeutronStartEOS.pdf

https://arxiv.org/abs/1603.02698

Thanks, George, for valuable information and links, mostly new for me, will have a look at it.

"as you add more mass, the radius decreases"

Up to now I understood Schwarzschild radius will linearly increase with mass, while radius of neutron star will increase by third root of mass only hence will be captured and hidden by event horizon beyond some critical mass.

JKF: Up to now I understood Schwarzschild radius will linearly increase with mass

Yes, that's right.

JKF: while radius of neutron star will increase by third root of mass

No, it decreases or is perhaps almost constant, but the detail depends on the equation of state, see the link. (Incidentally, in relation to the previous discussion, note that the gravitational binding energy given on that page is around 19%.)

There's a lot of research going into that equation (as you can see from the number of different curves people have calculated) because it depends in part on all sorts of exotic particles that may or may not exist. The particle physics guys have a real challenge there, but the bottom line is that as the mass increases, the internal pressure rises but the radius decreases slowly, becoming more rapid near the maximum mass, until the degeneracy pressure reaches its maximum. After that, the star cannot do anything but collapse to within the Schwarzschild radius.

You should also look into the regions just below the "black hole" shaded area on the chart, they indicate where the pressure would be infinite and a region where "causality would be violated", that means that the conditions would be such that speed of sound would exceed the speed of light (see the second link). Those set definite limits to the maximum stable radius/mass combination before the Schwarzschild radius.

https://en.wikipedia.org/wiki/Neutron_star#Gravity_and_equation_of_state

https://en.wikipedia.org/wiki/Equation_of_state#Ultrarelativistic_equation_of_state

Thanks, George, for additional material. I conclude that nature of neutron stars and black holes themselves is still a matter of controversial discussion, while the existence and behavior of binary black hole mergers and associated gravitational waves have allegedly been confirmed in detail by LIGO discoveries.

Theory says the waves modulate the transit time of the light Amrit, and it works.

"You seem to be under the impression that the loss of 3 solar masses occurs at the time of merger, that is not the case. That amount of energy is the total integrated over the inspiral and merger, the amount in the last few cycles is only a small part of it."

Dear George,

have you become aware of a recent paper entitled (see reference below):

LIGO’s “GW150914 signal” reproduced under YARK theory of gravity ??

Cited from abstract: "the binary merger necessitates a rest mass decrease in YARK (which we calculated to be about 3.1 solar masses on the whole) that we predict should be released via electromagnetic radiation emission according to our theory."

This finding stays in clear contradiction to your suggestion that 3 solar masses are totally converted into gravitational wave energy.

http://www.nrcresearchpress.com/doi/10.1139/cjp-2016-0699#.WfHxgYhpFb4