Heat flow components of Stress/Energy Tensor

Thread starter TerryW
Start date Oct 27, 2023
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Heat flow Physics

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The discussion revolves around the heat flux component of the Stress/Energy Tensor, specifically the equation q^i u^i + u^i q^i = 0. The user seeks clarification on this equation, referencing a source that states the heat flux is spacelike in the comoving frame, which they find unclear. The implication is that the heat flux vector q^i is orthogonal to the four-velocity u^i, leading to the conclusion that their dot product equals zero. Understanding this relationship is crucial for grasping the physical significance of the heat flux in the context of relativity. Further insights into the spacelike nature of heat flux in a comoving frame would enhance comprehension of the topic.

Oct 27, 2023

TerryW

Gold Member

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

Last edited: Oct 29, 2023

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