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Clarification of Terminology - GR Stress-Energy Tensor

  1. Feb 25, 2008 #1
    My current understanding of the components of the symmetric stress-energy tensor used in the Einstein Field Equations is:

    ex:
    [tex]T_{00}[/tex] is energy.

    [tex]T_{01}, T_{02}, T_{03}, T_{10}, T_{20}, T_{30}[/tex] is flux of energy, is momentum.

    [tex]T_{11}, T_{22}, T_{33}[/tex] is flux of momentum, is pressure.

    [tex]T_{12}, T_{13}, T_{23}, T_{21}, T_{31}, T_{32}[/tex] 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: [tex]T_{12}, T_{13}, T_{23}, T_{21}, T_{31}, T_{32}[/tex] 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: [tex]\frac{\partial f}{\partial x} + ...[/tex]) with flux? If so, is it correct to equate the Laplace operator (ex: [tex]\frac{\partial f^2}{\partial^2 x} + ...[/tex]) operator with diffusion? If so, is there an operator that denotes "flux of flux of flux" (ex: [tex]\frac{\partial f^3}{\partial^3 x} + ...[/tex])? If so, is there such an operator as [tex]\frac{\partial f^4}{\partial^4 x} + ...[/tex] ?

    Thank you for any information that you have.

    - Shawn
     
    Last edited: Feb 25, 2008
  2. jcsd
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