nLab stress-energy tensor

Idea

In a model (in theoretical physics) of gravity coupled to other fields, the energy momentum tensor or stress energy tensor T is the variation of the matter part $S_{fields}$ in the Einstein-Hilbert action with respect to the metric, $\delta S_{fields} = T \delta g$.

It is a measure for the energy and momentum density of the matter contribution to the theory.

Since the variation of the Einstein-Hilbert action $S_{EH}$ is the Einstein tensor $G$, the equations of motion of gravity, hence Einstein's equations assert that (up to constant prefactors)

$$G = T \,.$$

Properties

Renormalization and Vacuum energy

The renormalization freedom in perturbative quantization of gravity (perturbative quantum gravity) induces freedom in the choice of vacuum expectation value of the stress-energy tensor and hence in the cosmological constant.

For details see there.

Details

• For the scalar field: see at geometry of physics – A first idea of quantum field theory this example

Related concepts

• stress tensor

• energy-momentum relation

• Dirac current