General relativity with focus on action?

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Discussion Overview

The discussion centers around the approach to general relativity (GR) that emphasizes the action principle and its application in deriving equations of motion. Participants explore various resources and books that adopt this perspective, as well as the philosophical implications of using the action principle in the context of GR.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for books that focus on the action of fields in general relativity.
  • Another mentions that Dirac derives the equations of GR from the principle of action.
  • Several participants note that many GR textbooks, including those by Carroll, Wald, and d'Inverno, discuss the action principle.
  • A participant highlights Landau and Lifshitz's volume 2 as a favorite for introductory GR, emphasizing its use of the action principle to derive the Einstein field equations.
  • Another participant recommends "Introduction to General Relativity" by Bambi, which follows the Lagrangian formalism and the principle of least action.
  • There is a discussion about the characterization of Hilbert's action as heuristic versus formal, with differing opinions on the terminology based on individual preknowledge.
  • One participant argues that the action principle is a versatile tool for deriving equations of motion and finds it more intuitive than Einstein's derivation.

Areas of Agreement / Disagreement

Participants generally agree on the relevance of the action principle in the context of general relativity and the availability of resources that discuss it. However, there is disagreement regarding the characterization of Hilbert's approach as heuristic or formal, indicating differing perspectives on the interpretation of the action principle.

Contextual Notes

Some participants express varying levels of familiarity with the action principle, which may influence their interpretations and preferences for resources. The discussion reflects a range of opinions on the nature of heuristic versus formal approaches in the context of deriving equations in GR.

LCSphysicist
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I am having a class of general relativity. It seems that the professor will follow an approach which consist of achieve the action, and variate it to get the equations of motion (indeed, that's how we already got the geodesic equation, the dynamics of a particle in electromagnetism, the equation of the fields itself, and the action of massless particle, etc...). Do you know any book that follows such approach? That is, a book that focus mainly on the action of the fields itself.
 
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Dirac derives GR equations from the principle of action.
 
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Nearly every book on GR discusses the action: Carroll, Wald, d'Inverno, etc. Which book do you use?
 
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My favorite for introductory GR is Landau+Lifshitz vol. 2. He uses the action principle to derive the Einstein field equation. The Hilbert action is the most simple heuristic argument for why these equations should look as they look.
 
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Introduction to General Relativity by Bambi.

Excerpt from a book description:

"Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action."

I found the book quite readable and going
straight to its object.
 
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vanhees71 said:
My favorite for introductory GR is Landau+Lifshitz vol. 2. He uses the action principle to derive the Einstein field equation. The Hilbert action is the most simple heuristic argument for why these equations should look as they look.
I agree that LL vol 2 is good. You mention Hilbert action as a heuristic argument. Is heuristic the right word here. I thought of Einsteins intuitive manner of developing his equations as heuristic. I would regard Hilbert's development as quite formal.
 
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What you call "heuristic" is pretty much a question of your preknowledge. For me the action principle is the most versatile tool to guess equations of motion given a symmetry principle and I think it's much more "intuitive" or "heuristic" than Einstein's derivation.
 

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