?Gravity in 3D: Computing Degree of Freedom

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Discussion Overview

The discussion centers on understanding the degrees of freedom for gravity in three dimensions, particularly in the context of massless gravity and the implications for graviton propagation. Participants reference various texts to explore these concepts within theoretical frameworks.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why gravity in three dimensions does not have local degrees of freedom and seeks a method to compute these degrees of freedom for gravity in any dimension D.
  • Another participant cites Carlip's book on 2+1 quantum gravity, noting that in three dimensions, the Riemann tensor is determined by the Ricci tensor and the metric, leading to the conclusion that the Riemann tensor vanishes and thus there are no gravitational waves.
  • Multiple participants reference Zwiebach's book on string theory, which discusses the counting of degrees of freedom in phase space, indicating that this number is proportional to (D-3), suggesting no graviton propagation for D=3.
  • One participant mentions an additional book by John David Brown, indicating interest in further exploration of the topic.

Areas of Agreement / Disagreement

Participants generally agree on the lack of local degrees of freedom for gravity in three dimensions and the implications for graviton propagation, but the discussion remains open with references to various texts and interpretations.

Contextual Notes

The discussion relies on specific theoretical frameworks and assumptions about the nature of gravity in different dimensions, which may not be universally accepted or applicable across all contexts.

shereen1
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Dear all
can anyone help me to understand why gravity in 3 dim doesn't have local degree of freedom. How can i compute the degree of freedoms for gravity in and dimension D.
If i consider massless gravity in 3d is the graviton propagating
 
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See e.g.Carlip's book on 2+1 quantum gravity. In three dimensions, the Riemann tensor is completely determined by the Ricci tensor and the metric. Hence the vacuum einstein eqns state the Riemann tensor vanishes. Hence no gravitational waves.
 
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haushofer said:
See e.g.Carlip's book on 2+1 quantum gravity. In three dimensions, the Riemann tensor is completely determined by the Ricci tensor and the metric. Hence the vacuum einstein eqns state the Riemann tensor vanishes. Hence no gravitational waves.
Thank you haushofer i will download the book and have a look on it.
 
Zwiebach's book onstring theory has a nice exposition of the counting of degrees of freedom in phase space. This amount is proportional to (D-3). So no graviton propagation for D=3.
 
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haushofer said:
Zwiebach's book onstring theory has a nice exposition of the counting of degrees of freedom in phase space. This amount is proportional to (D-3). So no graviton propagation for D=3.
I will download it to, i also find the book of Steven Carlip interesting too!
Thank you for your time.
 
haushofer said:
Zwiebach's book onstring theory has a nice exposition of the counting of degrees of freedom in phase space. This amount is proportional to (D-3). So no graviton propagation for D=3.
Ther is also a book for John David Brown. It is interesting too.
 

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