Mordred

I concur I cannot think of any conjecture of gravity and gravitational radiation as being separate

Careful study.... (years of studying) (Yes some of what I claim is outside a single article... call it experience) Lets ask a question. What is the difference between a plasma cloud and a rock? The short answer density. (Aside from the particle closeness allows other interactions... strong and electromagnetic binding energy). Point being although the BH itself has greater density. Doesn't mean lower density relations in a larger volume cannot generate similar effects. Add the factor that any information beyond the EH (ie Mass) is lost to the system. Gravity propogates at speed of c. So it is equally affected by the geodesic equations that apply to light. Neither light nor mass escapes the EH (except via Hawking radiation). A simple line conclusion is that the surrounding regions outside the EH of each BH must be involved. (Excluding the mass inside the EH, which cannot escape...) Mass is an extremely misleading term. Probably the most accurate definition is "resistance to inertia change The mass of the Earth can create a BH. If it's volume falls under its Schwartzchild radius. Or even that a rock. Well let's just look at the amount of mass / energy is contained in just the accretion disk. (Careful it's a 900 page coverage) http://arxiv.org/abs/1104.5499 :''Black hole Accretion Disk'' -Handy article on accretion disk measurements provides a technical compilation of measurements involving the disk itself. You can have the mass of entire Suns outside the EH. In the accretion disk. Only a percentage falls beyond the EH. The rest being radiated away via the jets

The region between the two BH's is of a higher energy/density due to the spacetime curvature stress tensor. This region effectively has a mass of its own. See the Einstein ring. http://astrobites.org/2014/11/04/what-would-a-binary-black-hole-merger-look-like/ The Einstein ring is the spacetime distortions surrounding both BHs Here lets refer to the following statement. "Imagine observing a distant binary star and trying to measure the gravitational field at your location. It is the sum of the field from the two individual components of the binary, located at distances r1 and r2 from you. As the binary evolves in its orbit, the masses change their position with respect to you, and so the gravitational field must change. " The gravitational field is the regions inside and surrounding the Einstein ring. As its energy/density will gradually fall off to the background spacetime. If you look on page 6 Under Compact Binary system. The third equation applies the above statement. http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf What this means is any change within this system in angular monentum (including the average momentum of the particles within the system) can produce gravity waves. A good example is looking for gravity waves in the CMB. This isn't quite accurate. A BH doesn't lose mass from inside it's event horizon. (Except through Hawking radiation) The mass used to generate a G wave is from the surrounding spacetime. Including but not limiited to the accretion disk. In a binary system this is any higher energy/density region from the background metric. Aka the higher gravitational field from a flat Euclidean background field. This is why we define the system via the Einstein field equations and why there is no possibility of Shapiro delay.

No Strange understands one aspect you and Dan choose to ignore. The Einstein field equations already factor in time dilation effects. That includes Shapiro delay. I find it amazing how you two can ignore the equations (EFE) used on pages 6,7 and 8 which encompasses all coordinate orientations into 256 partial derivatives just under the [latex] T^{ij}[/latex] coordinates. The GRAVITY waves is the LOSS of Mass of the BINARY SYSTEM. Not the individual blackholes.

That's probably because your missing the connection between the amplitude of the signal and the angular momentum. Ask yourself this question "Which BH has more redshift/blueshift? Which one is moving faster than the other? The signal itself is emitted by the shared spacetime between BOTH BH's Why do you think the amplitude is calculated via loss of angular momentum of the system. See section 3.5 of the above link. http://relativity.livingreviews.org/open?pubNo=lrr-2009-2&page=articlesu27.html Here notice the seemingly random movement of spacetime outside the Einstein ring. http://apod.nasa.gov/apod/ap160212.html Here is a good example of the sinusoidal distortions. http://www.outerspacecentral.com/relativity_page.html these are due to the Quadrupole polarization strains

Polarization can be used to determine orientation. Here http://relativity.livingreviews.org/open?pubNo=lrr-2009-2&page=articlesu27.html

Do you understand the term waveform cycle? The period of a wave is the amount of time it takes to complete one cycle. Frequency is the number of complete cycles that a wave completes in a given amount of time. With say an alternator one cycle is one complete rotation and will produce a Dipolar (sinusoidal waveform). One maxima one minima. GW are not true sinusoidal waveforms they are distorted. However other than that article above I can't find good quadrupole waveform images (at least non digital) plenty of digital quadrupole. The complete 2 maxima and 2 minima occurs every cycle. Of each wave.

The only part you need is the image of a quadrupole waveform. It is not sinusoidal. But a distorted sinusoidal. The two maxima and minima occurs each chirp cycle. The maxima being a half cycle, the minima the second half cycle

See the paper I just posted Robitty.

Here this will probably help. http://www.google.ca/url?q=http://arxiv.org/pdf/1212.5553&sa=U&ved=0ahUKEwj_zLeCiMjLAhUUUWMKHTp4BfoQFggZMAI&usg=AFQjCNGKV4oABytsZQUuqj7sohSqCyM6dw note the distortions on the sinusoidal images. Those are quadrupole waveforms. A sinusoidal waveform from EM radiation is a dipole waveform. Chirp frequency the the rate an amplitude of each wave. Not the the wave characteristics.

The Maxima/minima determine the TYPE of waveform QUADRUPOLE. The rate and number of waveforms determine the chirp

Did you even look at the equations for chirp? This is already part of the equations. None of the 5 equations in that pdf require Shapiro delay and they also don't require supercomputers. (Not for chirp itself) Pages 6, 7 and 8.http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf The maxima and minima aspects deal with the TYPE of waveform. Not the rate each wave is emitted. (Quadrupole) Chirp is covered on page 10. Which is the rate each waveform is emitted

Yes but your both missing The fact that neither BH emits the chirp. The chirp is from the spacetime interactions between both BH's. So why would you have Shapiro delay?

Danp I think you missed a key detail. The two maxima and minima affect the polarization not the the chirp rate. The formulas for chirp rate are actually fairly simple.

Just the choice of counter model. Usually the counter model is more competitive. Ie LCDM vs MOND back when MOND was in stronger contention. Though I suppose Van's model may have been more supported at one time.

To understand that you would need to understand the term stellar aberration. https://en.m.wikipedia.org/wiki/Stellar_aberration_(derivation_from_Lorentz_transformation) In this case he is discussing aberration of gravity. The first link gives the general idea though. essentailly the paper is comparing the Lorentz invariance of light to gravity being variant or invariant. If the graviton is truly massless, just as light is then gravity would be invariant. The emitters velocity would have no influence upon the propogation of gravity. (Velocity dependant cancellations). If however gravity is not invariant then conservation of momentum can cause changes in the speed of the graviton. Most papers discuss alternative competing theories for comparison. This is essentially what this paper is doing. The comparison is Lorentz invariant or not invariant. For gravity. The paper includes electromagnetic Metrics to help explain the variance and invariant theories. The conclusion the paper presents is gravity is invariant. Essentially stating that the speed of gravity will be the same to all observers regardless of the observer or emitter velocities. I found it kind of humorous that the paper mentions Van Flandern... well you decide lol https://en.m.wikipedia.org/wiki/Tom_Van_Flandern

No he's saying there is some lag as defined by the speed of light. In this case the speed of gravity. The lag is what he's describing by retarded position

The time delay effects are already included in the [latex]T^{ij}[/latex] Formulas on page 8 That's the beauty of tensor usage in the Einstein field equations. You handle 4d coordinate change without specifically using a specific coordinate system

[latex]M_c =\frac{(m_1m_2)^{3/5}}{(m_1 + m_2)^{1/5}}[/latex] This is the formula for chirp mass. You can see both masses are included. The gravitational force is in the next three equations on that link you posted page 10. It already accounts for changes in orbit via two maxima and minimal values. "In practice what it means is that for each cycle made by the binary motion, the gravitational wave signal goes through two full cycles there are two maxima and two minima per orbit. For this reason, gravitational waves are called quadrupolar waves." See pages 6,7 and 8. Where you account for position of the two objects, they include the time components on page 8 The chirp formula relates to the number of waves which includes the polarization

No you obviously don't understand the Shapiro delay or the chirp. The Shapiro delay is essentially the time dilation due to travelling through a gravity well. Now in the Binary BH scenario NEITHER BH produces gravity waves. They are both symmetric rotating objects. The gravity waves emitted is due to the changes of the assymmetric spacetime changes encompassing BOTH BHs. So the Shapiro delay will be the same for all measurement points on the chirp signal. Not all objects emit gravity waves. Any symmetric rotating object of constant velocity will not produce waves.

Yes but that's not the chirp or not the rate the chirp occurs. See the equations page 10. http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf The Shapiro delay will affect how long it takes us to see each signal equally.

No the Shapiro delay and the chirp are two different things. A Shapiro delay will affect all frequencies and polarizations of the chirp equally. The paper you posted uses the quadrupole spin 2 statistics but doesn't state differences in each polarization (correctly so). " The chirp indicates that as gravitational waves are emitted, they carry energy away from the binary. The gravitational binding energy decreases, and the orbital frequency increases." See below paper on the chirp calculations in the pocket handbook section The Shapiro delay would have the same influence upon each emitted wave. http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf

The CoM is the sum of vector forces. It's the same thing. I've already given a simpler example. However if you want it worded in CoM terms each object will react to change when that object receives the information of a change. So the sum of forces (vectoral) will point to the retarded CoM position until the change in field strength reaches each object.

It's simple logic, the sum is the strength of the force of gravity by the signals you've received. This type of problem is common. Two body problem for example for orbits. Let's say you have a binary star system and one orbitting planet. The orbit is determined by the sum of gravity from both suns. The planet will react to changes with the appropriate delay for the gravitational force to arrive. For example if one star blew up, the planet will follow the path of the two star system until the loss of gravity reaches the planet then it will alter orbit.

I'm not sure why your having trouble. Both objects have sufficient time for their gravity to reach you so you can sum their values. The influence you feel is the position of where it was. We feel the effects of gravity from our sun 8 minutes ago, any change in potential would take 8 minutes to arrive. Same goes for object a and b. The gravitational changes will arrive from each object at different times. When you receive the change the value of the sum changes.