Implication of Tsallis entropy in the Thomas-Fermi model for self-gravitating fermions

The Thomas-Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics. Starting from the q-deformation of the Fermi-Dirac distribution function, a generalized Thomas-Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans' instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans' wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length.