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Trace of SEM tensor

1. jfy4

650
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,

2. atyy

10,133
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. atyy

10,133
Another random fact is that CFTs and Maxwell's equations have traceless SEMs.

4. jfy4

650
Thanks atyy for those references and tit-bits. I'm going to bump to see if I can get anything else.