Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Eager to learn 3+1 decomposition

  1. Nov 24, 2005 #1
    Eager to learn "3+1 decomposition"

    Is there any post, notes, books that gives complete introduction to "3+1 decomposition" in ADM fashion, as well as in tetrad formalism?
  2. jcsd
  3. Nov 24, 2005 #2


    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    this is something you might like to know, even though it does not exactly answer the question

    The Dynamics of General Relativity
    R. Arnowitt (Syracuse Univ.), S. Deser (Brandeis Univ.), C. W. Misner (Princeton Univ.)
    30 pages, no figures
    Journal-ref: "Gravitation: an introduction to current research", Louis Witten ed. (Wiley 1962), chapter 7, pp 227--265
    "This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@physics.umd.edu ."

    You are asking about the ADM formalism for Gen Rel.
    This paper is interesting because it is the first appearance of it, in a 1962 article by ADM themselves. It was recently scanned and made available electronically on arxiv, to provide "contemporary accessibility."

    I hope someone else can provide a link to a recent pedagogical exposition of ADM formalism. After 40 years there should be available some streamlined introductions and explanations, hopefully ONLINE so one does not have to rely on the usual hardcopy classics.

    BTW if you have access to a college or university library so that it would be convenient for you to consult hardcopy textbooks, did you look in MTW Gravitation (Misner, Thorne, Wheeler)?
    Last edited: Nov 24, 2005
  4. Nov 24, 2005 #3


    User Avatar
    Gold Member

    Peter Peldan, "Actions for Gravity, with Generalizations: A Review"
  5. Nov 24, 2005 #4


    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Hey kakarukeys, let's revise your original inquiry to get rid of the word "complete" and see if we get some more different suggestions. How about we change it to "nice easy"

    Garrett that Peldan article is formidable. It requires considerable self-confidence just to contemplate Figure 1 that shows all the various 3+1 Lagrangians and Hamiltonians for General Relativity and how they relate to each other. A rare and impressive thoroughness, in my humble.
  6. Nov 25, 2005 #5
    Ok thanks.
    Ya. Nice and Easy, with no or few omission of intermediate steps of calculations.
    I am following MTW on ADM formalism.
    I need comprehensive introduction to the same technique in Tetrad formalism. (You may call it Vierbeins, or Cartan's).
  7. Nov 25, 2005 #6
    I am a graduate students who are curious what's going on in LQG community, but only equipped with only general knowledge of differential geometry, general relativity, quantum field theory.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Eager to learn 3+1 decomposition
  1. Why 3+1 dimensions? (Replies: 29)