Michael Mozina wrote:
I do have a problem however with their "assumption' that more massive object always merger faster than smaller objects. That seems like an arbitrary assumption.
It's not an assumption.
Considering the number of different variables related to mass sizes, charges (if any), orbital aspects, accretion disk influences, spin rates, merger angles, etc, ya, it's an "assumption", probably many of them in fact.
The inspiral and merger of compact objects is caused by gravitational radiation described by the Einstein field equations. The inspiral would not happen in classical mechanics - it is a consequence of GR which you constantly claim to accept. GR predicts that rapidly rotating compact bodies will lose energy through gravitational radiation which will lead to their inspiral and ultimate merger. So, to calculate the characteristics of the inspiral phase, you need to solve the Einstein field equations.
Ok. Then again the more massive the objects the more momentum they contain and the more momentum they'd need to shed in the form of gravitational waves in order for them to merge.
There are no exact analytical solutions to the Einstein field equations for the two body problem, so theoreticians use approximations, called the post-Newtonian formalism, which are basically curtailed series expansions beyond the Einstein quadrupole formula of the metric tensor that describe how orbits depart from the classical form.
Ya, and I suspect that is where a lot of 'assumptions' have to be made, and where the oversimplifications probably take place.
The approximations become more and more accurate (they converge) for higher powers of v/c. So, for example, Einstein used expansion out to (v/c)2 in calculating the anomalous advance in the precession of Mercury and, in modern terminology, this is called 1PN. Calculations of inspiralling orbits are currently calculated out to 3.5PN or (v/c)7.
The calculations become increasingly lengthy and difficult for higher nPN even for equal mass circular orbits, and are complicated by unequal masses, elliptical orbits, and spinning bodies. Nevertheless, these calculations have been done for a vast range of conditions using numerical methods and computer power, and these are the templates used by LIGO and Virgo to match whitened strain data. The seminal paper that forms the foundation for this is Blanchet et al, Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order. There is a huge literature about the post-Newtonian formalism. It is these templates, based on GR, which show that more massive bodies have fewer gravitational wave cycles in the bandwidth of LIGO/Virgo. However that conclusion falls rather easily out of the Einstein quadrupole formula.
Unless you are highly competent in tensor analysis you are just going to have to accept those results.
I'm sorry, but I saw how LIGO siimply manipulated their sigma value by leaving out all environmental noise and making assumptions galore about blip transients. Mathematical models tend to get simplified to remove or oversimplify complications like charge, spin rates, merger angles etc. I'm inclined to believe that a lot of such 'oversimplication' would be required to be able to claim that massive objects always merge more "quickly" than lower mass objects. Even just the charge of the black holes could have an influence. Similarly charged black holse would tend to repel one another, whereas oppositely charged black holes would merge faster and be attracted to one another. It's complicatons like these which probably have to simply be ignored to come up with a 'one size fits all" math formula related to black hole mergers.
It's ironic that you are engaged in a campaign to get EU/PC people to accept GR (which doesn't seem to be going too well), whilst calling a rather obvious consequence of applying GR to orbital mechanics an "assumption".
You folks have a very bad habit of "lumping together" a whole lot of assumptions under the umbrella of "GR theory", like your insertion of magical forms of matter and energy into a supernatural blunder theory while trying to pass it off as GR theory and trying to ride the coattails of GR. I've come to doubt that your folks really care about the core aspects of GR vs. the "completely made up" metaphysical nonsense that you try to stuff into such formulas while still trying to ride the scientific coattails of GR theory.
Admittedly I have some reading to do about how they come up with such numbers and I thank you for your references as to where I might start, but just looking at it logically, it seems highly likely that many dubious "assumptions" would be required to come up with a "one size fits all" mass merger model which requires all massive objects to merge faster than lower mass objects.
IMO you should be happy that at least a few EU/PC proponents are big fans of GR theory, and they can tell the difference between the core aspects of GR, and the supernatural nonsense that is called 'LCDM" theory. Otherwise, I think everyone would agree that a theory that is 95 percent metaphysical bathwater should just be tossed out entirely. That's probably why GR has such a bad rap in our community. Not everyone takes the time to study GR and understand where GR ends and LCMD magic theory begins.