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A symmetric rank-2 tensor in relativity, which expresses the flux of energy-momentum along timelike and spacelike axes. Also known as the stress tensor or the energy-momentum tensor. In the Einstein field equations, it is the source of gravitational fields.
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Confusion regarding 4-Velocity Derivative Identity (for conservation of energy momentum tens...
During Carroll's discussion of the energy-momentum tensor for a perfect fluid (page 36), he writes out that its divergence should be zero. He then expands this as follows:
$$\partial_\mu T^{\mu\nu} = …