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Finding stress energy tensor of a rod under tension

  1. Apr 25, 2012 #1
    I am given a rod with mass per unit length [itex] \mu [/itex], cross sectional area A, and under a tension F. I am also told that the tension F is uniform over the cross sectional area A. Find the stress energy tensor inside the rod.

    I know that for the stress energy tensor [itex] T^{00}[/itex] gives the energy density, [itex] T^{0i}[/itex] gives the energy flux through a i-surface, [itex] T^{i0}[/itex] gives the i-momentum density, and [itex] T^{ij}[/itex] gives the i-momentum flux through a j-surface.

    I have that [itex] T^{00} = \mu / A [/itex] and that [itex] T^{0i} = T^{i0} = 0 [/itex] since the rod is stationary so the particles have no net momentum. As for [itex] T^{ij} [/itex], if i assume that the rod is lying lengthwise along the x axis, then [itex] T^{11} = F/A [/itex] since the momentum flux is the momentum per unit time per unit area or in other words the force per unit area. Then it seems to me that [itex] T^{ij} = 0 [/itex] for all other entries since the tension acts along the x direction.

    Therefore the stress energy tensor only has 2 nonzero entries on the main diagonal, and the rest of the entries are 0. Am I missing something here? It seems too simple a form to have and I am not sure if i took everything into account.
     
  2. jcsd
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