3

I'm after any in-depth expositions on Noether's Theorems, especially graduate-level textbooks, which include application/discussion in a general relativistic context. Strangely enough I don't see it explicitly mentioned in for example Misner Thorne and Wheeler. I assume there is a relation to the usual presentation of Killing vector fields and the stress-energy tensor conservation.

Qmechanic
  • 201,751
qwerty
  • 59
  • Noether's theorem famously fails for GR; Killing vector fields are obviously picking up where the pieces of Noether's theorem broke off, but even trying to define energy is a difficult process in GR. – naturallyInconsistent Dec 08 '23 at 05:50
  • Suggestion: To focus the question consider to only ask about a GR context. – Qmechanic Dec 08 '23 at 06:12
  • @naturallyInconsistent I'm not sure why you need to define energy to work with Noether's theorem and symmetries in general. It's also interesting you say that Noether's theorem "fails" for GR when from what I have been able to gather "by Noether’s Second Theorem, the corresponding conservation law is trivial, meaning that it vanishes on all solutions." This is different in spirit and meaning to "failing". In addition, the upvoted answer here seems to suggest differently https://physics.stackexchange.com/a/177978/92181 – qwerty Dec 08 '23 at 06:18
  • Related: https://physics.stackexchange.com/q/98798/2451 – Qmechanic Dec 08 '23 at 08:06
  • 1
    A short summary (so it is not “in-depth”) for the role of Noether's theorems in GR is Deser 2019. – A.V.S. Dec 09 '23 at 08:55
  • wondering if @user_35 has suggestions, as they wrote a lengthy answer in the other thread – qwerty Dec 27 '23 at 22:35

0 Answers0