Understanding the Trace of the SEM Tensor

In summary, the discussion revolves around the stress-energy momentum tensor and its relationship to the Ricci tensor and scalar in the context of general relativity. The mention of Nordstrom's scalar gravitation, a previous theory of gravity, and its connection to the trace SEM is also brought up. The conversation also touches on connections between CFTs and Maxwell's equations and their traceless SEMs.
  • #1
jfy4
649
3
Hi,

Let [itex]T_{\alpha\beta}[/itex] be the stress-energy momentum tensor. What does [itex]g_{\alpha\beta}T^{\alpha\beta}[/itex] 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 [itex]T[/itex] say?

Thanks,
 
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  • #2
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
 
  • #3
Another random fact is that CFTs and Maxwell's equations have traceless SEMs.
 
  • #4
Thanks atyy for those references and tit-bits. I'm going to bump to see if I can get anything else.
 

1. What is a SEM tensor?

A SEM tensor, or stress-energy-momentum tensor, is a mathematical object used in the field of general relativity to describe the distribution of mass, energy, and momentum in space-time. It is a symmetric tensor with 10 components, representing the 10 independent components of the gravitational field.

2. How is the SEM tensor related to Einstein's field equations?

Einstein's field equations, which describe the relationship between matter and the curvature of space-time, can be derived from the SEM tensor through a mathematical process known as the Einstein tensor. This shows the crucial role that the SEM tensor plays in understanding the gravitational field.

3. What is the physical significance of the trace of the SEM tensor?

The trace of the SEM tensor represents the energy density of the gravitational field. This means that it measures the amount of energy per unit volume that is present in the gravitational field at a given point in space-time. It is an important quantity in understanding the overall energy distribution in the universe.

4. How is the trace of the SEM tensor related to the cosmological constant?

The cosmological constant, which is a parameter in Einstein's field equations, can be expressed in terms of the trace of the SEM tensor. This means that the value of the cosmological constant is related to the overall energy density of the universe. A non-zero cosmological constant is believed to contribute to the acceleration of the expansion of the universe.

5. Can the SEM tensor be used to describe other physical phenomena besides gravity?

Yes, the SEM tensor can also be used to describe the energy, momentum, and stress associated with other physical fields, such as electromagnetic fields. In this context, it is known as the electromagnetic stress-energy tensor. However, the SEM tensor is most commonly used in the study of gravity and general relativity.

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