Everything about The Stress-energy Tensor totally explained
The
stress-energy tensor (sometimes
stress-energy-momentum tensor) is a
tensor quantity in
physics that describes the
density and
flux of
energy and
momentum in
spacetime, generalizing the
stress tensor of Newtonian physics. It is an attribute of
matter,
radiation, and non-gravitational
force fields. The stress-energy tensor is the source of the
gravitational field in the
Einstein field equations of
general relativity, just as mass is the source of such a field in
Newtonian gravity.
Definition
Please note that throughout we'll assume the use of the Einstein summation notation. When using coordinates, x0 will represent time, while the other coordinates x1, x2 and x3 will be the remaining spatial components.
The Stress-energy tensor is defined as the
tensor
where S
matter is the nongravitational part of the
action. This is symmetric and gauge-invariant. See
Einstein–Hilbert action for more information.
Belinfante-Rosenfeld stress-energy tensor
This is a symmetric and gauge-invariant stress energy tensor defined over flat spacetimes. There is a construction to get the Belinfante-Rosenfeld tensor from the canonical stress-energy tensor. In GR, this tensor agrees with the Hilbert stress-energy tensor. See the article
Belinfante-Rosenfeld stress-energy tensor for more details.
Pseudotensors
All useful
pseudotensors in general relativity are
stress-energy-momentum pseudotensors, of which the
Einstein pseudotensor and the
Landau-Lifschitz pseudotensor are examples.
Further Information
Get more info on 'Stress-energy Tensor'.
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