= Neutrino tensor anisotropic stress
{title2=$\pi_\nu^{ij}$}
For massless <neutrinos> with a temperature perturbation $\Theta$ and background <energy density> $\bar\rho_\nu$, the physical trace-free spatial <stress-energy tensor> is
$$
\pi_\nu^{ij}=4\bar\rho_\nu\int\frac{d\Omega_e}{4\pi}
\Theta\left(e^ie^j-\frac13\delta^{ij}\right).
$$
Some conventions define $\Pi^{ij}=-\pi_\nu^{ij}$ and correspondingly reverse the sign of the stress source in the gravitational-wave equation.
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