# Clarification of Terminology - GR Stress-Energy Tensor

1. Feb 25, 2008

### shalayka

My current understanding of the components of the symmetric stress-energy tensor used in the Einstein Field Equations is:

ex:
$$T_{00}$$ is energy.

$$T_{01}, T_{02}, T_{03}, T_{10}, T_{20}, T_{30}$$ is flux of energy, is momentum.

$$T_{11}, T_{22}, T_{33}$$ is flux of momentum, is pressure.

$$T_{12}, T_{13}, T_{23}, T_{21}, T_{31}, T_{32}$$ is diffusion of momentum, is viscosity.

My questions are:
1) Is pressure (the flux of momentum) the diffusion of energy?
2) Is viscosity (the diffusion of momentum) the flux of pressure?
3) If 1 and 2 are true, is it accurate to call diffusion "the flux of flux"?
4) If 3 is true, does "the flux of flux of flux" have a name?

ex: $$T_{12}, T_{13}, T_{23}, T_{21}, T_{31}, T_{32}$$ is the flux of flux of flux of energy, is diffusion of momentum, is the flux of pressure, is viscosity.

5) Is it correct to equate the "del" operator (ex: $$\frac{\partial f}{\partial x} + ...$$) with flux? If so, is it correct to equate the Laplace operator (ex: $$\frac{\partial f^2}{\partial^2 x} + ...$$) operator with diffusion? If so, is there an operator that denotes "flux of flux of flux" (ex: $$\frac{\partial f^3}{\partial^3 x} + ...$$)? If so, is there such an operator as $$\frac{\partial f^4}{\partial^4 x} + ...$$ ?

Thank you for any information that you have.

- Shawn

Last edited: Feb 25, 2008