  The statistical mechanics of a cloud of particles interacting via their
gravitational potentials is an old problem which encounters some issues when
the traditional Boltzmann-Gibbs statistics is applied. In this article, we
consider the generalized statistics of Tsallis and analyze the statistical and
thermodynamical implications for a self-gravitating gas, obtaining analytical
and convergent expressions for the equation of state and specific heat in the
canonical as well as microcanonical ensembles. Although our results are
comparable in both ensembles, it turns out that only in the canonical case the
thermodynamic quantities depend explicitly on the non-extensivity parameter,
indicating that the question of ensemble equivalence for Tsallis statistics
must be further reviewed.
