- #1
Azrael84
- 34
- 0
Hi,
How would go about arguing that the Stress-Energy tensor is actually a tensor based on how it must be linear in both it's arguments?
I'm thinking it requires one 1-form to select the component of 4-momentum (e.g. [tex] \vec{E}=<\tilda{dt} ,\vec{P}> ) [/tex] and also one 1-form to define the surface (e.g [tex] \tilda{dt} [/tex] defining surfaces of constant t, so giving us densities etc).
I know that [tex] T^{\alpha \beta}=T(\tilda{dx^{\alpha}}, \tilda{dx^{\beta}}) [/tex]. Not sure how one would argue that it therefore must be linear in these arguments?
How would go about arguing that the Stress-Energy tensor is actually a tensor based on how it must be linear in both it's arguments?
I'm thinking it requires one 1-form to select the component of 4-momentum (e.g. [tex] \vec{E}=<\tilda{dt} ,\vec{P}> ) [/tex] and also one 1-form to define the surface (e.g [tex] \tilda{dt} [/tex] defining surfaces of constant t, so giving us densities etc).
I know that [tex] T^{\alpha \beta}=T(\tilda{dx^{\alpha}}, \tilda{dx^{\beta}}) [/tex]. Not sure how one would argue that it therefore must be linear in these arguments?