Eager to learn 3+1 decomposition

In summary, Garrett's article is a comprehensive guide to ADM formalism for General Relativity. It is a difficult technique and requires a lot of self-confidence to even contemplate Figure 1. However, it is a rare and impressive thoroughness.
  • #1
kakarukeys
190
0
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?
 
Physics news on Phys.org
  • #2
kakarukeys said:
Is there any post, notes, books that gives complete introduction to "3+1 decomposition" in ADM fashion, as well as in tetrad formalism?

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

http://arxiv.org/abs/gr-qc/0405109
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:
  • #4
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"

Is there any post, notes, books that gives nice easy introduction to "3+1 decomposition" in ADM fashion, as well as in tetrad formalism?

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.
 
  • #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).
 
  • #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.
 

What is "Eager to learn 3+1 decomposition" and why is it important?

"Eager to learn 3+1 decomposition" is a mathematical method used in machine learning and data analysis to decompose datasets into smaller, more manageable subsets. It is important because it allows for more efficient and accurate analysis of complex data, making it an essential tool for scientists in various fields.

How does "Eager to learn 3+1 decomposition" work?

The method works by breaking down a large dataset into smaller subsets based on a specific criteria, such as correlations between variables or patterns in the data. These smaller subsets are then analyzed separately, allowing for a more in-depth understanding of the data.

What are the benefits of using "Eager to learn 3+1 decomposition"?

Aside from increasing efficiency and accuracy in data analysis, "Eager to learn 3+1 decomposition" also allows for improved interpretability of results. It can also help identify hidden patterns or relationships within a dataset that may have been overlooked through other methods.

Are there any limitations to using "Eager to learn 3+1 decomposition"?

Like any method, "Eager to learn 3+1 decomposition" has its limitations. It may not be suitable for all types of datasets and may not always provide the most optimal results. It also requires a certain level of knowledge and expertise in mathematics and data analysis to properly implement and interpret the results.

How is "Eager to learn 3+1 decomposition" different from other decomposition methods?

One key difference is that "Eager to learn 3+1 decomposition" is a greedy algorithm, meaning it makes decisions based on the current best option without considering future implications. Other decomposition methods may take a more holistic approach. Additionally, "Eager to learn 3+1 decomposition" specifically focuses on decomposing datasets into smaller subsets, while other methods may have different objectives such as dimensionality reduction or feature selection.

Similar threads

  • Beyond the Standard Models
Replies
15
Views
3K
  • Special and General Relativity
Replies
5
Views
270
Replies
2
Views
606
  • Differential Geometry
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Quantum Physics
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
949
  • Differential Geometry
Replies
2
Views
897
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top