Trace of SEM tensor


by jfy4
Tags: tensor, trace
jfy4
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#1
Oct27-11, 10:38 PM
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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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atyy
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#2
Oct27-11, 11:18 PM
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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
atyy
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#3
Oct28-11, 01:27 AM
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Another random fact is that CFTs and Maxwell's equations have traceless SEMs.

jfy4
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#4
Oct31-11, 09:01 AM
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Trace of SEM tensor


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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