Timeline for The speed of gravitational waves in general relativity
Current License: CC BY-SA 3.0
9 events
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| Nov 11, 2012 at 15:33 | comment | added | user21349 | @Leonard says, "Without weak-field assumptions, the problem of finding the speed of a wave makes no sense at all." Igor Khavkine says, "The definition of speed of propagation I gave works independent of whether the metric is dynamical..." IMO both are true. Naively we would like to split the spacetime into background and wave parts, and define the speed of the wave using the metric of the background. We can't do that in strong-wave gravity. All we can do is the much less ambitious thing defined by Igor Khavkine. | |
| Nov 11, 2012 at 13:15 | comment | added | Leonard | @Igor: Thanks! The preprint looks good. | |
| Nov 11, 2012 at 13:14 | vote | accept | Leonard | ||
| Nov 11, 2012 at 11:12 | comment | added | Igor Khavkine | Also, these ideas about the speed of propagation of linear vs non-linear waves/disturbances and its dependence of a background (non dynamical) or dynamical metrics are contained within the theory of the domain of dependence of quasilinear hyperbolic systems. I recommend looking this up in the references I gave above for more detail. Also, at the risk of shameless self-promotion, these ideas are covered in Secs.3 and 4 of this recent preprint: arxiv.org/abs/1211.1914 | |
| Nov 11, 2012 at 10:59 | comment | added | Igor Khavkine | @Ben, the speed propagation that I had in mind was the "fastest" one possible. So a trailing sub-light speed tail does not affect that. I think that's physically reasonable. @Leonard: The definition of speed of propagation I gave works independent of whether the metric is dynamical (GR or GR+Maxwell) or not (just Maxwell). You used the term "static", but "non dynamical" is I think more appropriate. | |
| Nov 11, 2012 at 3:46 | comment | added | Leonard | On a further note, as our measuring instruments are ultimately affected by spacetime curvature, what does it mean to measure the speed of a gravitational wave? | |
| Nov 11, 2012 at 3:41 | comment | added | Leonard | @Ben: Yes, I was assuming a background-independent spacetime. Am I right to say the following? (1) Under weak-field assumptions, we have a stationary background spacetime with respect to which the actual dynamic spacetime can be studied as perturbations using linearization, in which case the problem of finding the speed of a wave is well-posed. (2) Without weak-field assumptions, the problem of finding the speed of a wave makes no sense at all. | |
| Nov 11, 2012 at 2:42 | comment | added | user21349 | But note that the definition you've given for the speed of propagation does not necessarily map cleanly onto the question as naively stated. For example, GR predicts that a gravitational-wave pulse propagating on a background of curved spacetime develops a trailing edge that propagates at less than c. This doesn't contradict your analysis, but one might consider it to be a counterexample, depending on how the OP's statement is construed. The problem with the naive question is that it assumes a background spacetime with a metric that can be used to define speeds. | |
| Nov 10, 2012 at 22:34 | history | answered | Igor Khavkine | CC BY-SA 3.0 |