
#55
Feb2013, 05:29 PM

Sci Advisor
PF Gold
P: 4,860





#56
Feb2013, 05:32 PM

Sci Advisor
PF Gold
P: 4,860

Maybe if you could point to some reference on this? I remain very interested whether there is some way to 'rescue' EP and some form of geodesic motion for similar mass two body problem  but gave up on it when last studying this issue. 



#57
Feb2013, 05:33 PM

Physics
Sci Advisor
PF Gold
P: 5,504

However, he also mentions numerical solutions at the end, which makes me wonder: do numerical solutions not give enough information to even apply the test I described? 



#58
Feb2013, 05:43 PM

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P: 8,004





#59
Feb2013, 05:45 PM

Sci Advisor
PF Gold
P: 4,860





#60
Feb2013, 05:54 PM

Sci Advisor
PF Gold
P: 4,860





#61
Feb2013, 06:02 PM

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P: 8,004

Intuitively, I'd expect that for nonzero mass, but the taking the test body approximation (body is not a source), then we get an exact timelike geodesic. Then if we allow backreaction (body is a source), then we get an approximate timelike geodesic. 



#62
Feb2013, 06:12 PM

Physics
Sci Advisor
PF Gold
P: 5,504





#63
Feb2013, 06:26 PM

Sci Advisor
PF Gold
P: 4,860





#64
Feb2013, 06:28 PM

Sci Advisor
PF Gold
P: 4,860





#65
Feb2013, 06:38 PM

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P: 8,004





#66
Feb2013, 06:44 PM

Sci Advisor
PF Gold
P: 4,860

http://arxiv.org/abs/1002.5045 Which is based on Gralla and Wald, is a bit simpler and easier to understand. They make explicit that mass must decrease to zero as λ decreases to zero. 



#67
Feb2013, 07:03 PM

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P: 8,004





#68
Feb2013, 08:06 PM

Sci Advisor
P: 8,004

It seems conceptually ok to have the "word description" of λ→0 as size going to zero, we allow the point particle to be a black hole, and we end up with nonzero mass M≠0. 



#69
Feb2013, 09:04 PM

Sci Advisor
PF Gold
P: 4,860

"The results of this section (i.e., the results of sec. IV of [4]) may be summarized as follows. Consider a oneparameterfamily of spacetimes containing a body whose size and mass decrease to zero, according to the stated assumptions." "Furthermore, the “particle mass” M is indeed the ADM mass of the body (as measured in the scaled limit)." All of this must be true based on my physical argument: you cannot treat a finite mass body as not being a source, no matter how small you make it (without also decreasing its mass). 



#70
Feb2013, 09:17 PM

Sci Advisor
PF Gold
P: 4,860

Then, a world line representing a body trajectory is one that is always inside a world tube of nonvanishing SET (call it a matter region). What would need to be shown is that there exists a timelike geodesic in matter region that remains always in the matter region. Then if the matter size is small, this is reasonably a body trajectory. I am unaware of any such result being referred to in the literature. It would be really cool if it were true and someone provided a convincing argument for it. Then, also, a timelike geodesic in the vaccuum region would represent a test body trajectory. Another take on this would be to imagine coorbiting spherical shells. Then also what we would like to believe is that some geodesic inside each shell (one with the right initial tangent) is always inside the shell, never hitting the edge. (Note that while for one shell, you have Minkowski space inside, for two shells you do not  there is no such thing as a gravity shield, and one shell influences geometry inside the other shell). 



#71
Feb2113, 04:39 AM

P: 2,889

Ultimately this might be a definitional problem, but if you want to call geodesic motion to all orbiting bodies, extended or test particles, regardless of the intensity of the radiation (gravitational or EM) they are emitting you basically are saying that all test particles and extended bodies worldlines following some kind of orbit no matter how unstable are following geodesic motion wich I don't think it's true. I used to also think that extended objects in orbit followed geodesics but was convinced here at PF that this would make gravitational radiation a superfluous notion since if orbiting bodies emitting radiation, regardless of the intensity(strongfield case) didn't see affected their geodesic motion, first:what could actually ever affect a geodesic path? and second: how do we expect that radiation to affect distance bodies detectors if it isn't capable to alter the geodesic path of the emitting body in the least(as long as we still consider third Newton's law as valid of course). 



#72
Feb2113, 05:00 AM

P: 2,889

This post from Wald's collaborator Sam Gralla might be relevant here:
http://physicsforums.com/showpost.ph...30&postcount=9 


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