Heat flow components of Stress/Energy Tensor

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SUMMARY

The discussion centers on the components of the Heat Flux Stress/Energy Tensor, specifically the equation q^i u^i + u^i q^i = 0. TerryW seeks clarification on this equation, referencing the text "Problem Book in Relativity and Gravitation" by Lightman et al., which states that q^α u_α = 0, indicating that heat flux is spacelike in the comoving frame. This implies that the heat flux vector q^i is orthogonal to the four-velocity u^i, leading to the conclusion that the inner product results in zero.

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  • Understanding of four-vectors in relativity
  • Familiarity with the Stress/Energy Tensor in physics
  • Knowledge of spacelike and timelike vectors
  • Basic concepts of heat flux in relativistic contexts
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TerryW
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Homework Statement
Show that the Trace of the Heat Flux Stress/Energy Tensor is zero
Relevant Equations
T(heat) = q^i u^j + u^i q^j
I'm pretty sure I understand why q^i u^j + u^i q^i is the stress component (i \neq j) of the Heat Flux Stress/Energy Tensor but I can't think of, or find any explanation for why q^i u^i + u^i q^i = 0.

I found one reference in Lightman, Press, Price and Teukolsky - Problem Book in Relativity and Gravitation which just says
"Since q^α u_α = 0 (heat flux is spacelike in comoving frame)" but what does that really mean from a physics point of view?

Can anyone help?TerryW

PS - Preview doesn't seem to be working at the moment
 
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