  The nonextensive kinetic theory for degenerate quantum gases is discussed in
the general relativistic framework. By incorporating nonadditive modifications
in the collisional term of the relativistic Boltzmann equation and entropy
current, it is shown that Tsallis entropic framework satisfies a H-theorem in
the presence of gravitational fields. Consistency with the 2nd law of
thermodynamics is obtained only whether the entropic q-parameter lies in the
interval $q \in [0,2]$. As occurs in the absence of gravitational fields, it is
also proved that the local collisional equilibrium is described by the extended
Bose-Einstein (Fermi-Dirac) q-distributions.
