This question is a little vague and I hope I can put across what I am looking for without too much confusion.

What is the motivation behind studying asymptotic symmetry groups in the context of general relativity? How is it important in the AdS/CFT correspondence? I have also read that the study of the ASG plays a role in understanding scattering as well. Why?

NOTE: I know what the ASG is. At least I think I do. I do not want to know how one goes about deriving it, etc. I am asking a more general question about the motivation behind its study. Indeed I am more interested in the motivations to study outside of the AdS/CFT correspondences and the likes. However, if you think the derivation of the ASG gives one some insight into this question, then please also mention that as well.

PS - I am not just interested in the ASG of AdS space. I simply mentioned an example here.

  • $\begingroup$ On the AdS/CFT side, are you looking for something more than a discussion of how the asymptotic symmetry algebra of a given bulk spacetime matches the symmetry of the dual CFT? $\endgroup$ – joshphysics Jul 23 '13 at 4:21
  • $\begingroup$ The asymptotic symmetry group is one of the things that define the superselection sector of the theory. The physical Hilbert space of states preserving this group is a representation of this group. $\endgroup$ – Luboš Motl Jul 23 '13 at 4:30
  • $\begingroup$ Can you explain the term "superselection sector of the theory"? $\endgroup$ – Prahar Jul 23 '13 at 4:55
  • $\begingroup$ At the beginning of this presentation, there are apparently interesting references. It seems that we may have a correspondance between asymptotic flat spaces ( Bondi–Metzner–Sachs symmetry Group) and relativist, or non-relativist conformal theories. $\endgroup$ – Trimok Jul 23 '13 at 11:24
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    $\begingroup$ @dingo_d From a pure GR point of view I think this is a standard reference home.uchicago.edu/~geroch/P464/AsympStr.pdf $\endgroup$ – ungerade Jan 30 '14 at 0:24

To my understanding, motivations for studying Asymptotic Symmetries in General Relativity has to do with trying to define global conservation laws. Since conserved quantities are linked to symmetries of spacetime through Killing vector fields, if you want to define the total "mass" or "energy" of the universe you need to make sure that your spacetime has no energy content at infinity, so it is asymptotically flat, i.e. similar [in a way to be defined by the ASG] to Minkowski spacetime.

Another thing is that you may have asymptotic symmetries along different directions: spatial versus null infinity. And so the total "energy" enclosed by a spacetime has different interpretations depending on the kind of infinity you use.

Finally, I think it was proven that the difference between the total energy content of a spacetime at spatial infinity and that at null infinity is the total amount of gravitational radiation emitted at any time. I am quite rusty on the subject, but when I studied it the two names in the literature were Abhay Ashtekar and Robert Geroch.


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