Gravitational wave generation of integrating blackholes

[Growl]

I see it stated repeatedly that the integration of two black holes would generate a huge gravitational wave, however since the falling spiral of the two would be 180 degrees out of phase, would not the resulting gravitational wave represent only the difference in mass of the two?

[mistermack]

I know nil about black holes colliding or Gravitational Waves, but when two collide, I'm picturing that a vast amount of kinetic energy has to go somewhere, and would that add to the total mass of the system? 

[Genady]

Here is the exact answer (36.16a):

where

[swansont]

What would the phase of the spiral have to do with anything? 

[Growl]

20 minutes ago, swansont said:

What would the phase of the spiral have to do with anything? 

Wave A with energy x combined with wave B with energy x’ (equal energy, 180 degrees phase difference) would produce a resultant wave C with 0 energy. If A and B had different energies, wave C would represent the difference in energies, not the sum.

Also the resultant C would not be a pure sine wave but rather constituted of components representing the frequencies: Af, Bf, Af - Bf and Af + Bf.

Edited September 19, 2023 by Growl
More info

[swansont]

2 hours ago, Growl said:

Wave A with energy x combined with wave B with energy x’ (equal energy, 180 degrees phase difference) would produce a resultant wave C with 0 energy. If A and B had different energies, wave C would represent the difference in energies, not the sum.

Also the resultant C would not be a pure sine wave but rather constituted of components representing the frequencies: Af, Bf, Af - Bf and Af + Bf.

Black holes are not waves

[Markus Hanke]

14 hours ago, Growl said:

Wave A with energy x combined with wave B with energy x’ (equal energy, 180 degrees phase difference) would produce a resultant wave C with 0 energy.

For a BH merger, there is only one wave field, not two, so I’m not sure what you mean by ‘phase difference’.

Also, gravitational waves and the energy-momentum they ‘carry’ do not add linearly (GR isn’t a linear theory), so the argument wouldn’t hold anyway.

[Growl]

21 hours ago, swansont said:

Black holes are not waves

This discussion is about the gravity wave created by the integration of two black holes

 

8 hours ago, Markus Hanke said:

For a BH merger, there is only one wave field, not two, so I’m not sure what you mean by ‘phase difference’.

Also, gravitational waves and the energy-momentum they ‘carry’ do not add linearly (GR isn’t a linear theory), so the argument wouldn’t hold anyway.

There is only one gravitational wave field in the universe… There are two entities contributing to the resultant wave “C” these two entities are exclusive to their local time/space. The observer of the resultant gravitational wave is distant, so GR linearity has nothing to do with the subject of the resultant gravitational wave.

On 9/19/2023 at 5:26 PM, Genady said:

Here is the exact answer (36.16a):

where

Good stuff, however it does not consider phase relationship for the resultant.

 

On 9/19/2023 at 5:09 PM, mistermack said:

I know nil about black holes colliding or Gravitational Waves, but when two collide, I'm picturing that a vast amount of kinetic energy has to go somewhere, and would that add to the total mass of the system? 

I do not believe it would add to the mass, rather the rotation of the system, when the integration is complete a single rotating mass would not create a wave and only the gravitational wave created by shifting position of the two before integration would be in evidence. If the two were equal in mass, the receding influence of one would be exactly mirrored by the other and the resulting cg would not change, hence no resultant wave, however if the masses were different, the shift of the cg would be indicative of the difference.

[swansont]

1 hour ago, Growl said:

This discussion is about the gravity wave created by the integration of two black holes

Then what is “since the falling spiral of the two would be 180 degrees out of phase, would not the resulting gravitational wave represent only the difference in mass of the two?” referring to? The gravitational waves do not undergo a “falling spiral”

(and it’s gravitational wave; a gravity wave is something different)

Quote

Good stuff, however it does not consider phase relationship for the resultant.

The phase relationship of what? There is no combination of waves here.

[Growl]

27 minutes ago, swansont said:

Then what is “since the falling spiral of the two would be 180 degrees out of phase, would not the resulting gravitational wave represent only the difference in mass of the two?” referring to? The gravitational waves do not undergo a “falling spiral”

(and it’s gravitational wave; a gravity wave is something different)

The phase relationship of what? There is no combination of waves here.

There are two entities whose interaction produces the resultant gravitational wave. As they approach one another they will spiral in until integrated. 
 

The phase relationship of the gravitational shift resulting from the two black holes is 180 degrees out of phase as one approaches an outside observer the other recedes.

Edited September 20, 2023 by Growl

[swansont]

51 minutes ago, Growl said:

There are two entities whose interaction produces the resultant gravitational wave. As they approach one another they will spiral in until integrated. 

 

And there is no phase involved in this.

51 minutes ago, Growl said:

 

The phase relationship of the gravitational shift resulting from the two black holes is 180 degrees out of phase as one approaches an outside observer the other recedes.

Where did you get this drawing?

[Growl]

https://www.google.com/imgres?imgurl=https%3A%2F%2Fmedia-cldnry.s-nbcnews.com%2Fimage%2Fupload%2Ft_fit-760w%2Cf_auto%2Cq_auto%3Abest%2FMSNBC%2FComponents%2FPhoto%2F_new%2F120816-Waves1Photo-hmed-0815a_files.jpg&tbnid=t6MdMgD6Hcq2oM&vet=12ahUKEwj-5q6tsrqBAxUhIGIAHTzSCckQMygtegUIARCzAg..i&imgrefurl=https%3A%2F%2Fwww.nbcnews.com%2Fid%2Fwbna48689955&docid=YtHnZa0nUPZ5ZM&w=760&h=760&q=spiral of orbiting black holes&hl=en-US&ved=2ahUKEwj-5q6tsrqBAxUhIGIAHTzSCckQMygtegUIARCzAg

The origin is from NASA, a government agency

Edited September 21, 2023 by Growl

[Genady]

6 hours ago, Growl said:

Good stuff, however it does not consider phase relationship for the resultant.

If I understand your question correctly, then this diagram answers it. See the parts (d) and (e). The source of the waves is on the left, the faraway receptor is on the right:

and the explanations:

As you see, in the first approximation, i.e., in the dipole case (d), the contributions cancel exactly even for different masses, contrary to your assumption in the OP ("the difference in mass of the two"). The outgoing wave survives because of the quadrupole (e).

Edited September 21, 2023 by Genady

[Growl]

Indeed! I was mistaken, they do cancel regardless a difference in mass… a shift in phase however would produce a wave.

 

If I read correctly angle theta is the incline of the orbital plane relative to the observer?

 

I will need to peruse further after some rest.

In my humble opinion no energy would be lost via gravitational wave as the two integrate, rather the new entity would achieve greater or perhaps lose spin… comment?
 

Also in my opinion, you are very astute and have a fine abstract mind. My own weakness is expressing myself mathematically, although I can envision the physical from the math.

Thank you for your interest.

 

[studiot]

10 hours ago, swansont said:

(and it’s gravitational wave; a gravity wave is something different)

Thank you for pointing this out; I'm sure I made this mistake a few times in ignorance.  +1

 

Quote

https://medcraveonline.com/PAIJ/about-the-nature-of-gravitational-and-gravity-waves.html

Introduction. The terms of gravity waves and gravitational waves are two commonly confused terms in physics. Gravity waves are generated in fluid mediums or on interfaces between two fluid mediums. On the other hand, gravitational waves are produced by cosmological phenomena in the universe

 

Perhaps this LIGO article might help the discussion

@Growl  did you mean the third one on the list  inspiral  ?

 

Quote

https://www.ligo.caltech.edu/page/gw-sources

 

Astronomers have defined four categories of gravitational waves based on what object or system generates the waves: Continuous, Compact Binary Inspiral, Stochastic, and Burst.

 

 

 

Edited September 21, 2023 by studiot

[Growl]

Yes of course inspiral. Thank you, a very good article.. I am foolishly investigating if photons could be very short wavelength gravitational waves.

[swansont]

11 hours ago, Growl said:

https://www.google.com/imgres?imgurl=https%3A%2F%2Fmedia-cldnry.s-nbcnews.com%2Fimage%2Fupload%2Ft_fit-760w%2Cf_auto%2Cq_auto%3Abest%2FMSNBC%2FComponents%2FPhoto%2F_new%2F120816-Waves1Photo-hmed-0815a_files.jpg&tbnid=t6MdMgD6Hcq2oM&vet=12ahUKEwj-5q6tsrqBAxUhIGIAHTzSCckQMygtegUIARCzAg..i&imgrefurl=https%3A%2F%2Fwww.nbcnews.com%2Fid%2Fwbna48689955&docid=YtHnZa0nUPZ5ZM&w=760&h=760&q=spiral of orbiting black holes&hl=en-US&ved=2ahUKEwj-5q6tsrqBAxUhIGIAHTzSCckQMygtegUIARCzAg

The origin is from NASA, a government agency

"An artist's impression of gravitational waves from two orbiting black holes."

This shows the black holes and the gravitational waves, not black holes as waves. 

[Growl]

1 hour ago, swansont said:

"An artist's impression of gravitational waves from two orbiting black holes."

This shows the black holes and the gravitational waves, not black holes as waves. 

I never said the black holes were waves. I do see where you are misled, when I state “wave A” I am referring to the wave constituent produced by black hole “A”, I apologise.

Edited September 21, 2023 by Growl