  New exact solutions of the modified Dirac equation describing a neutrino with
nontrivial electromagnetic properties in extreme background conditions are
obtained. Within the quasi-classical treatment the effective Lorentz force that
describes the neutrino propagation in the magnetized rotating matter is
introduced. We predict the effect of the spatial separation of different types
of relativistic neutrinos and antineutrinos (different in flavors and energies)
by the magnetized rotating matter of a star. Low energy neutrinos can be even
trapped inside the star. We also predict two new phenomena: a new type of the
neutrino electromagnetic radiation (termed "Light of (milli)Charged Neutrino",
$LC\nu$) and a new mechanism of the star angular velocity shift due to
neutrinos escaping the star (termed "Neutrino Star Turning" mechanism, $\nu S
T$). The possible impact of the $\nu S T$ mechanism on a supernova explosion
yields a new astrophysical limit on the neutrino millicharge
$q_{\nu}<1.3\times10^{-19}e_0$. In addition, the $\nu S T$ mechanism can be
also used to explain the origin of pulsar "anti-glitches" and ordinary glitches
as well.
