I found the following definitions:

  • The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime.

  • Flux is a simple and ubiquitous concept throughout physics and applied mathematics describing the flow of a physical property in space, frequently also with time variation. It is the basis of the field concept in physics and mathematics.

So I presume from above that the property which flows in GR is energy and/or momentum. Is this a correct?

Under what circumstances does it flow? and from where to where?


1 Answer 1


The stress-energy tensor describes the flow of 4-momentum through spacetime. Without worrying too much about index placement or order, let's say $T^{\mu\nu}$ is the flux of $\mu$-momentum in the $\nu$-direction.

When $\mu$ is a spatial index, this is a component of ordinary $3$-momentum, and when $\mu$ is the time index we can call the flowing quantity energy.

Similarly, when $\nu$ is spatial we have a flux in a spatial direction (technically, across a surface whose normal is spacelike). When $\nu$ is the time index the quantity is flowing in the time direction, and we can call this a density.

Thus $T^{00}$ is energy density, $T^{0i}$ is the flux of energy in the $i$-direction, $T^{i0}$ is $i$-momentum density, and $T^{ij}$ is the $j$-flux of $i$-momentum.

The distinction between flow of $3$-momentum and flow of energy is a somewhat artificial remnant of Newtonian thinking, as is the distinction between fluxes in spatial directions and densities of quantities.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.