  Extremely compact objects trap gravitational waves or neutrinos, assumed to
move along null geodesics in the trapping regions. The trapping of neutrinos
was extensively studied for spherically symmetric extremely compact objects
constructed under the simplest approximation of the uniform energy density
distribution, with radius located under the photosphere of the external
spacetime; in addition, uniform emissivity distribution of neutrinos was
assumed in these studies. Here we extend the studies of the neutrino trapping
for the case of the extremely compact Tolman VII objects representing the
simplest generalization of the internal Schwarzschild solution with uniform
distribution of the energy density, and the correspondingly related
distribution of the neutrino emissivity that is thus again proportional to the
energy density; radius of such extremely compact objects can overcome the
photosphere of the external Schwarzschild spacetime. In dependence on the
parameters of the Tolman VII spacetimes, we determine the "local" and "global"
coefficients of efficiency of the trapping and demonstrate that the role of the
trapping is significantly stronger than in the internal Schwarzschild
spacetimes. Our results indicate possible influence of the neutrino trapping in
cooling of neutron stars.
