trapped modes of gravitational waves could influence some instabilities in these objects [@Abr-etal:1997:CLAQG:]. Trapping of neutrinos can be of high importance in the interior of the ECS: first, it will suppress the neutrino flow as measured by distant observers and, second, it can influence cooling of the ECS in a layer extending from some radius depending on details of their structure up to the surface radius. The cooling process could even be realized in a “two-temperature” regime, when the temperature profile in the interior of the star with no trapped neutrinos differs from the profile established in the external layer with trapped neutrinos [@Stu-Tor-Hle-Urb:2009:] modifying substantially the standard picture of the neutron star structure as given in [@Gle:1992:PHYSR4:; @Gle:2000:CompactStars:; @Hae-Zdu:1986:NATURE:; @Web-Gle:1992:ASTRJ2:; @Web:1999:Pul:]. In a different context, trapping of neutrinos inside rotating neutron stars has been discussed in [@Mallick-etal:2009:arXiv:0905.3605:].

The approximation of free, geodetical motion of neutrinos in the internal spacetime could be used when the mean free path of neutrinos $\lambda > R$. Neutrinos have inelastic scatter on electrons (muons) and elastic scatter on neutrons. The scatter cross section on electrons (neutrons) $\sigma_\mathrm{e}$ ($\sigma_\mathrm{n}$) determines the mean free path by formula $\lambda = \left(\sigma_{i} n_{i}\right)^{-1}$ where $n_i$ ($i = \mathrm{e, 