
#73
Feb2113, 07:20 AM

Sci Advisor
P: 8,004





#74
Feb2113, 07:25 AM

Sci Advisor
PF Gold
P: 4,860





#75
Feb2113, 07:38 AM

Sci Advisor
P: 8,004





#76
Feb2113, 03:09 PM

Sci Advisor
PF Gold
P: 4,860

One thing that prevents any possibility of such a limiting process approaching a null geodesic is that there is no such thing, in GR, of an 'almost null' timelike path, in any coordinate independent sense. So you must get a limiting timelike path, as the physics suggests.




#77
Feb2113, 03:34 PM

Sci Advisor
P: 8,004





#78
Feb2113, 03:43 PM

Physics
Sci Advisor
PF Gold
P: 5,505

Similarly, the two neutron stars in the binary pulsar could be following geodesics, but still have their orbital parameters change, because the metric is changing. In fact, that's probably the wrong way to think about it, though, because the changes in the orbital parameters, at least to a first approximation, *are* the changes in the metric. The stars themselves don't change, considered in isolation; what changes is their relationship. The overall metric of the system as a whole includes the relationship between the stars, so if that changes, the metric changes, even if each star remains exactly the same internally. This doesn't mean the stars don't travel on geodesics; it means that there is a single selfconsistent solution realized by Nature (which we can only approximate at our current level of knowledge) that has each star (more precisely, each star's center of mass) traveling on a geodesic of the full, timedependent metric that is ultimately due to the two stars acting together as sources. But *why* would the orbital parameters change, if the stars themselves are not changing internally? AFAIK the answer to this involves the lightspeed time delay in the propagation of gravity, as outlined, for example, in this paper by Carlip: http://arxiv.org/abs/grqc/9909087 Of course it's possible that the full, selfconsistent solution realized by Nature does not have the stars traveling on exact geodesics of the full, timedependent metric; that's what Gralla seems to think, for example. We won't know for sure until we can construct such solutions and make more precise observations. But I don't think we can rule out the possibility that, at least for systems like the binary pulsar, gravitational waves can be emitted without requiring any deviation from geodesic motion to explain them. 



#79
Feb2113, 03:45 PM

Sci Advisor
PF Gold
P: 4,860





#80
Feb2113, 04:00 PM

Sci Advisor
P: 8,004





#81
Feb2113, 04:01 PM

Sci Advisor
PF Gold
P: 4,860

If you try an averaging approach, how do you make it precise? Average of a bunch of convoluted geodesics? If the approach only applies to sufficiently simple SET, it isn't much of aresult. 



#82
Feb2113, 04:10 PM

Sci Advisor
PF Gold
P: 4,860

And if I imagine limiting this to zero sized stars, at every stage, vaccuum geodesics near a star represent a test particle orbit, while the star itself becomes singular. 



#83
Feb2113, 04:34 PM

Physics
Sci Advisor
PF Gold
P: 5,505

It is true that, since the star has finite size, no portion of the star other than its CoM will travel along a geodesic; again, that's obvious just by considering that the proper acceleration of any piece of matter at r > 0 must be nonzero. So there are certainly pieces of matter present that are traveling on nongeodesic worldlines. But if we don't need to worry about the star's internal structure, we can ignore all that, and just treat the motion of the star's CoM as the motion of the star. What I'm hypothesizing is that a similar dodge will work in a case like the binary pulsar: we can ignore the internal structure of the two neutron stars and treat the motion of each star's CoM as the motion of the star itself. Then the question becomes: what is the proper acceleration of each star's CoM? I'm hypothesizing that it's still zero; the only thing that I can see that would make it nonzero is that curvature effects would cause a net force on the star as a whole, something like "spacetime swimming": http://dspace.mit.edu/handle/1721.1/6706 In the binary pulsar case I would expect any effect of this type to be too small to matter because the separation between the stars is so much larger than their sizes; but I admit I have not tried to do any calculation along these lines. 



#84
Feb2113, 04:52 PM

Sci Advisor
PF Gold
P: 4,860

Well, for starters, there are big problems defining COM in GR. In any case, I assume you no longer would claim you know that this will work.
Last night I did find an old write up by Synge of the following: Under very broad assumptions, given a matter world tube with sharp boundary, and assuming no nongravitational radiation, and an exterior vaccuum metric region with no assumptions made (e.g. could be non static; no asymptotic flatness assumed), then there exists in the matter world tube a locus of points of no proper acceleration that form a continuous curve*. However, he claimed (without showing it, only by reference to ancient literature he was borrowing the treatment from) that such a locus not only need not be the path of any matter, it could be spacelike! (Even though every piece of matter is following a timelike path). * For a nonspinning body, it is necessary to assume things about pressure that seem physically plausible, to get this result. For a spinning body, he had to assume a limit on amount of spin. Without assuming these, it did not follow that there was a locus of noacceleration at all. So, I think you have a lot of work to make your argument really convincing. 



#85
Feb2113, 04:53 PM

P: 2,889

If GW are disturbances of the gravitational field i.e propagation of changes in spacetime curvature, it is hard to see how it would be possible for them to be emitted and detected maintaining geodesic motion of the body that emits them or the detector that receives them as long as we think of geodesics as the straightest spacetime lines in a curved manifold. 



#86
Feb2113, 05:15 PM

Physics
Sci Advisor
PF Gold
P: 5,505





#87
Feb2113, 05:22 PM

Physics
Sci Advisor
PF Gold
P: 5,505





#88
Feb2113, 05:33 PM

Sci Advisor
PF Gold
P: 4,860

I did find a way to visualize this surprising claim: Imagine there is fluid wave motion inside the body. Then the locus no acceleration could reflect that some 'particle' in the wave has no proper acceleration, while a nearby particle in a slightly different phase of the wave is the 'next' particle with no proper acceleration. Then the locus of no acceleration represents something more like a phase propagation than a material propagation. I can imagine it in a spacelike zigzag through the world tube. Perhaps under much more restrictive assumptions about the SET, you could get a nicer result. But, again, I've looked and not found any sign of such claim in the literature (but I don't have access to a university library, and don't claim to any great searching skills). [In particular, I did a lot of searching on 'generalized equivalence principle' and 'DetweilerWhiting' to see if there even any proposals that these could be generalized. I found none. The implications of some writers was clearly that this could only be expected for the extreme mass ratio case covered by the MiSaTaQua equation. ] 



#89
Feb2113, 06:07 PM

P: 2,889





#90
Feb2113, 06:11 PM

Sci Advisor
P: 8,004

http://arxiv.org/abs/1206.6538 has interesting comments about GW from binaries.



Register to reply 
Related Discussions  
Should a stationary charge on the earth radiate?  Special & General Relativity  12  
Does a charged particle in free fall radiate?  Special & General Relativity  4  
Does a coaccelerated charge radiate?  Classical Physics  19  
Does a uniformly accelerating charge radiate?  Classical Physics  24  
When does a charge radiate?  Special & General Relativity  55 