Understanding the Trace of the SEM Tensor

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    Sem Tensor Trace
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Discussion Overview

The discussion revolves around the interpretation and implications of the trace of the stress-energy momentum tensor (SEM) in the context of general relativity (GR) and its relation to the Ricci tensor and scalar. Participants explore theoretical connections and historical perspectives without reaching a consensus.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Historical

Main Points Raised

  • One participant questions the meaning of the expression g_{\alpha\beta}T^{\alpha\beta} and its relation to the Ricci tensor, suggesting a conceptual link between the SEM and curvature.
  • Another participant mentions that in Nordstrom's scalar gravitation, the trace of the SEM can be reformulated using the Ricci scalar, noting that while it is historically significant, it does not match observational data.
  • A third participant points out that conformal field theories (CFTs) and Maxwell's equations are characterized by traceless SEMs, introducing a different perspective on the properties of the SEM.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the SEM and the Ricci tensor, and there is no consensus on the implications of the trace of the SEM. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion does not clarify the assumptions underlying the relationship between the SEM and curvature, nor does it resolve the implications of the trace in different theoretical frameworks.

jfy4
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Hi,

Let T_{\alpha\beta} be the stress-energy momentum tensor. What does g_{\alpha\beta}T^{\alpha\beta} mean? I have always thought of the Ricci tensor and the SEM as the same thing essentially, but the Ricci scalar essentially assigns a number to the curvature of the manifold, what does T say?

Thanks,
 
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I don't know in GR, but Nordstrom's scalar gravitation, the first consistent relativistic theory of gravity, can be reformulated using the Ricci Scalar and the trace SEM. It doesn't match observation, but it's historically interesting.

See Eq 16 of http://arxiv.org/abs/gr-qc/0405030
 
Another random fact is that CFTs and Maxwell's equations have traceless SEMs.
 
Thanks atyy for those references and tit-bits. I'm going to bump to see if I can get anything else.
 

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