- #1
Jonsson
- 79
- 0
Hello there,
I am learning GR and in the cosmology chapter, we are using the metric
$$
ds^2 = - dt^2 + a^2(t) \left[ \frac{dr^2}{1 - \kappa r^2} + r^2 d \Omega \right].
$$
Suppose now that ##U^\mu = (1,0,0,0)## and the energy momentum tensor is
$$
T_{\mu \nu} = (\rho + p)U_\mu U_\nu + p g_{\mu \nu}.
$$
My professors says that this implies ##T^{\mu \nu} = \mathrm{diag}(\rho, p,p,p)##. Surely this is a typo, or is it just me that don't understand how to raise indecies? Thanks
I am learning GR and in the cosmology chapter, we are using the metric
$$
ds^2 = - dt^2 + a^2(t) \left[ \frac{dr^2}{1 - \kappa r^2} + r^2 d \Omega \right].
$$
Suppose now that ##U^\mu = (1,0,0,0)## and the energy momentum tensor is
$$
T_{\mu \nu} = (\rho + p)U_\mu U_\nu + p g_{\mu \nu}.
$$
My professors says that this implies ##T^{\mu \nu} = \mathrm{diag}(\rho, p,p,p)##. Surely this is a typo, or is it just me that don't understand how to raise indecies? Thanks