Anisotropic fermionic matter in a general relativistic framework and dynamic stability of anisotropic systems

In this paper we study nonrotating, spherical, gravitational equilibrium configurations of a semidegenerate collisionless Fermi gas, in a general relativistic framework. We consider a modified Fermi-Dirac distribution function, including an energy cutoff term to ensure solutions with finite mass and radius, as well as a second term taking into account the effect of the anisotropy with prevalence of transverse component of velocity. The problem of the dynamical stability is also considered in Newtonian regime by introducing a general criterion, for the anisotropic systems, in terms of adiabatic indexes.