Mordred

To be honest you would have a far easier time understanding how gravitational waves work if you focus on the energy/density not mass. Your question is better described in what are the energy/density distribution changes.

I like your answer Migl it's well thought out. I think I'll wait to see how much the OP understood before adding to your excellent explanation. +1

A massive particle will never reach c.

To understand my post two, The formula here best correlates. Then look at the SI base units for energy/density. Correct but again this doesn't mean that gravitational waves are only emitted during the event horizons merging. Which is the point I was trying to explain in the first place lol

Are you referring to where the mass is in the interior of a BH? Ie the singularity or entirety of the interior. We don't know. We can only hypothesize. We have no data of the interior conditions beyond the event horizon. Ah ok. The answer given by Strange is more accurate. Yes the the energy/density increases as you approach the event horizon. Its in a sense controversial to say the mass density via the energy/mass equivalence increases. In some ways GR doesn't have a clear cut definition of mass. For the purpose of what your trying to understand I would go with the reply by Strange

Is there a specific aspect your looking at that you perceive is different from my replies to Strange replies?

We would love to be able to gather datasets beyond the event horizon. It would have incredible applications towards quantum gravity etc. The accretion paper I posted earlier this thread also suggests a possible method to garnish data of the interior of an event horizon. If I recall it was in section 6. Again hypothetically. I'm not sure about that without examining the paper

Essentially the mass of the blackhole defines the radius that the event horizon will occur. Whether or not the interior of the BH is solid or singular (which we don't know) makes no difference to the Schwartzchild radius. We can only estimate the total mass of the BH by its Schwartzchild radius.

Energy/density has the same units as pressure. The SI unit is joules/m^3. https://en.m.wikipedia.org/wiki/Energy_density Trying to define how thick the event horizon is ? Is rather pointless. Once you cross the outer surface for lack of better terminology the information is lost to us. We simply cannot retrieve any details past the surface. Of course we also avoided talking about the amount of redshift involved. As much as the Schwartzchild metric has its inherent problems it's probably the best starting point to understanding the event horizon. I would suggest trying to understand that metric.

No it was related to Imaatsfal's post Though it does relate to how energy of a binary system can radiate prior to the event horizons meeting.

Oh I wouldn't worry I may have given you a couple of rep points however they were due to the quality of your posts The funny aspect about rep points is that I've found they don't reflect the quality of a post. More often than not I've received rep points by pointing out how foolish a poster is. Not necessarily in a polite format. Quite frankly the rep system is a poor judgement of post quality I've yet to see the rep system encourage quality of posts on any of the multiple forums I'm a member of. Science oriented or otherwise. Yes a series of poor quality or foolish posts can quickly gain bad rep points. However truly good quality posts may or may not gain a rep point. Quite frankly the whole gender/rep point gain aspect is foolish as well as well as reflecting sexual discrimination. Not on any fault of the female participants.

Understood. Takes time to equate all the needed equations onto an excel spreadsheet. Personally I like Scilab which is similar to mathlab. However the programming lanquage gets complex.

Ah I like my avatar. Suits the evil son of King Arthur. (Mordred) but lost in thought. If that costs me potential rep points so be it lol

Yes but part of the problem you were having was the radiated mass. In order to calculate the radiated mass you must calculate the total mass of the BINARY SYSTEM. Each wave emits a portion of that total mass. In other words every wave emits a %. So after each wave is emitted you must recalculate the total mass to calculate the emitted mass of the next wave. Which isn't as easy as it sounds as you need to account for kinetic as well as potential energy of the binary system. This is why you see an increase in amplitude of the waveform page 11 The change in frequency is due to chirp frequency including the ringdown phase http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf I hope you understand that now.

Still lol strain occurs every cycle of a frequency. Ringdown is a measure of frequency changes. That was why I was confused by your use of the polarity formula Which is handy to visualize a single wave. But frequency involves multiple waves. So does ringdown

I still think you were using the wrong equation for the ringdown phase. But here you decide. http://www.google.ca/url?q=http://arxiv.org/pdf/1506.00560&sa=U&ved=0ahUKEwjt-JTCtuzLAhVH42MKHb36DhsQFggcMAM&usg=AFQjCNFB0NtD0cy_mhjGnaTAh2RDLNKdIg See equation 6 Which is the equation to model the ringdown waveform. Note the similarities to the chirp formulas page 10 and 11? http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf But I guess I don't know what I'm talking about

You keep trying to model the cosmological constant via blackholes. Your attempts with Hawking radiation won't work either. The reason being is Hawking radiation only occurs when the blackbody temperature of the Universe is lower than the blackbody temperature of the blackhole. you would need blackholes smaller than the mass of the moon for this to occur with the BLACKBODY temperature today of the Universe. At the time of surface of last scattering that small blackhole would grow not evaporate. https://en.m.wikipedia.org/wiki/Hawking_radiation

No geodesics are rather tricky to derive but the related formulas are here. https://en.m.wikipedia.org/wiki/Geodesics_in_general_relativity Should be noted there is often more than 1 geodesic. Photons follow null geodesics.

That's not what the Pauli exclusion principle states.

There is so many mistakes in this last post I don't Even know where to start. Quite frankly in your case any reply I can give you would fall on deaf ears. Your blinded by your imagination, and lack of willingness to learn. Any ways should you choose to learn correctly the links I provided this thread is a good start

I think the equation that may suit best on energy/density to curvature relations may be better seen here. [latex]R_{ab}-\frac{1}{2}Rg_{ab}=8\pi GT_{ab}[/latex] [latex]R_{ab}[/latex] is the ricci tensor,[latex] g_{ab}[/latex] is the curved by the presence of energy via the stress tensor [latex]T_{ab}[/latex]. G is the gravitational constant. R is the ricci scalar. Conceptually this equation means curvature=energy... Equation 1.1 the curvature equals energy statement is footnote 1.2. http://www.google.ca/url?q=http://www.physics.usyd.edu.au/~luke/research/masters-geodesics.pdf&sa=U&ved=0ahUKEwj25uq8qOzLAhVM4WMKHWm4Ca0QFggRMAA&usg=AFQjCNEr4WEHhcvoL-LVhqBLVIcgBRFdkQ Now as I understand the Schwartzchild metric it assumes the background vacuum =0. However I don't believe it states the curvature has zero energy/density. Without going into energy being a property lets avoid gravitons and use gravitational field energy. (Of course we could get into Komar,Bondi and ADM mass but I don't we really need to.) As it would be off the OP topic https://en.m.wikipedia.org/wiki/Mass_in_general_relativity

Yeah I've had this argument before on physicsforum. The problem I've always had with the Schwartzchild child metric is the assumption of Euclidean flat being of zero energy density. At no point in the universe is there a zero energy/density. There is always the presence of some non zero field, for example the Higgs field itself. The term vacuum doesn't mean zero energy/density. Thankfully we can set the background metric as zero even if the background metric is a positive energy/density.

Here is the stress/energy tensor relations to the energy density and pressure. [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex] what this equation means is that as the gravitational potential increases So does the energy/mass density

Even the cosmological constant has positive energy density Carrock. A void region in space away from all sources of gravitational energy has an average energy density of 7.52 *10 ^-10 joules/ m^3. You can calculate that value via the critical density formula Which correlates to roughly 5 protons per m^3. The average energy density of the interstellar medium within galaxies being a higher energy density. On average 15 times higher. As you approach a massive object the average energy/density increases via the stress/energy tensor

Gravity doesn't get out the event horizon. The information of the mass of the singularity is in the gravitational field at the event horizon. Not in,