Symmetry of the Gravitational Stress Energy pseudo tensor

Asked Jun 05 '15 at 08:37

Active Jun 05 '15 at 13:34

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Recently, I have been reading on the Gravitational Stress-Energy pseudo tensor. It says in Wikipedia that one of the conditions for a suitable GSE pseudo tensor is that it has to be symmetric about the indices.

$$U_{\mu\nu} = U_{\nu\mu}$$

Why should this be the case?

edited Jun 05 '15 at 13:34

Qmechanic

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asked Jun 05 '15 at 08:37

Horus

As I recall, if it is not symmetric angular momentum would not be conserved. However I don't have the details to hand so I'm unwilling to risk a full answer. – John Rennie Jun 05 '15 at 09:06
@JohnRennie: The relevant wiki article does invoke angular momentum conservation as the argument, but omits details. – Kyle Kanos Jun 05 '15 at 13:15
Related: http://physics.stackexchange.com/q/68564/2451 and links therein. – Qmechanic Jun 05 '15 at 13:37
I see. I'll do some more deeper research. – Horus Jun 06 '15 at 13:14

Symmetry of the Gravitational Stress Energy pseudo tensor

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