ADM Formalism: Intro-to-Intermediate Explanation

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Discussion Overview

The discussion centers around the ADM formalism in the context of understanding the Alcubierre warp drive. Participants explore resources and texts that could aid in comprehending the ADM formalism, particularly for someone with a background in general relativity but lacking specific knowledge of ADM. The scope includes theoretical aspects of general relativity and its applications in advanced topics like warp drives.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant seeks resources for understanding the ADM formalism, noting their background in general relativity up to certain topics.
  • Another participant suggests focusing on the 3+1 split rather than the entire ADM formalism, recommending numerical relativity texts, including those by Alcubierre.
  • A different participant mentions Wald's discussion on the initial value formulation of general relativity, indicating it may be accessible without requiring extensive high-level mathematics.
  • One participant reiterates the suggestion to look at numerical relativity books, including Alcubierre's work, expressing a realization about not considering Alcubierre's texts earlier.

Areas of Agreement / Disagreement

Participants generally agree on the relevance of the 3+1 split and the usefulness of numerical relativity texts, but there is no consensus on the best approach or resource for understanding the ADM formalism specifically.

Contextual Notes

Limitations include the varying levels of mathematical prerequisites for different texts and the specific focus on the 3+1 split versus the full ADM formalism, which may affect the accessibility of the resources suggested.

Who May Find This Useful

Readers interested in general relativity, numerical relativity, or advanced theoretical physics, particularly those looking to understand the ADM formalism and its applications in concepts like the Alcubierre warp drive.

DEvens
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TL;DR
Looking for a description of the ADM formalism for somebody who as studied some GR
So I'm reading about the Alcubierre warp drive. And it's presented in the ADM formalism.

https://en.wikipedia.org/wiki/Alcubierre_drive
And I realize that understanding it is being slowed by my not having studied the ADM formalism. So, is there a good text or website or such, that does a good explanation of the ADM formalism? I have been through the basics of GR but didn't do that. Basically I got up to Oppenheimer-Schneider dust clouds, and interior solutions for spherically symmetric stars and such like topics. So I'm looking for something that an undergrad 3rd or 4th year could use.
 
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What you need is the 3+1split rather than all of the ADM formalism. You could take a look at any numerical relativity book, including Alcubierre's.
 
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I just took a look at Wald's discussion of the GR initial value formulation. It may not be totally out reach. It does not seem to require as much high level math as some other sections in Wald do.
 
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martinbn said:
What you need is the 3+1split rather than all of the ADM formalism. You could take a look at any numerical relativity book, including Alcubierre's.

Now, why didn't I think of looking for a book by Alcubierre? I never got off Arxiv.org. Thanks!
 

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