Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions Original Research Article

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the image-statistics. Starting from the image-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 image-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 image is traced. It is found that the image-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length.