3+1 decomposition of the stress-energy tensor
= 3+1 decomposition of the stress-energy tensor
Relative to a future unit normal $n^\mu$, the stress-energy tensor decomposes as
$$
T_{\mu\nu}=\rho n_\mu n_\nu+j_\mu n_\nu+n_\mu j_\nu+S_{\mu\nu},
$$
where $j_\mu$ and both indices of $S_{\mu\nu}$ are spatial.