- #1
tetris11
- 23
- 0
Okay so I have:
Eqn1) Tij=[tex]\rho[/tex]uiuj-phij = [tex]\rho[/tex]uiuj-p(gij-uiuj)
Where Tij is the energy-momentum tensor, being approximated as a fluid with [tex]\rho[/tex] as the energy density and p as the pressure in the medium.
My problem:
Eqn2) Trace(T) = Tii = gijTij = [tex]\rho[/tex]-3p
My attempt:
Tr(T) = Tii = gij[[tex]\rho[/tex]uiuj-p(gij-uiuj)]
= [[tex]\rho[/tex]gijuiuj-pgijgij+pgijuiuj)]
= [tex]\rho[/tex]u - p + pu
which doesn't equal rho-3p (eqn2) as required, so I've done something wrong.
I think I've contracted incorrectly but I don't know why... please help?
Eqn1) Tij=[tex]\rho[/tex]uiuj-phij = [tex]\rho[/tex]uiuj-p(gij-uiuj)
Where Tij is the energy-momentum tensor, being approximated as a fluid with [tex]\rho[/tex] as the energy density and p as the pressure in the medium.
My problem:
Eqn2) Trace(T) = Tii = gijTij = [tex]\rho[/tex]-3p
My attempt:
Tr(T) = Tii = gij[[tex]\rho[/tex]uiuj-p(gij-uiuj)]
= [[tex]\rho[/tex]gijuiuj-pgijgij+pgijuiuj)]
= [tex]\rho[/tex]u - p + pu
which doesn't equal rho-3p (eqn2) as required, so I've done something wrong.
I think I've contracted incorrectly but I don't know why... please help?