  We study the weak decay of the neutral pion to a neutrino-antineutrino pair,
$\pi^0\to \nu \bar{\nu}$, in the Skyrme model. In baryon free-space the process
is forbidden by helicity while in a dense baryonic medium, the process becomes
possible already to leading order in $G_F$ due to the break-down of Lorentz
symmetry in the background medium.
