Gravitational instabilities of isothermal spheres in the presence of a
  cosmological constant
  Gravitational instabilities of isothermal spheres are studied in the presence
of a positive or negative cosmological constant, in the Newtonian limit. In
gravity, the statistical ensembles are not equivalent. We perform the analysis
both in the microcanonical and the canonical ensembles, for which the
corresponding instabilities are known as `gravothermal catastrophe' and
`isothermal collapse', respectively. In the microcanonical ensemble, no
equilibria can be found for radii larger than a critical value, which is
increasing with increasing cosmological constant. In contrast, in the canonical
ensemble, no equilibria can be found for radii smaller than a critical value,
which is decreasing with increasing cosmological constant. For a positive
cosmological constant, characteristic reentrant behaviour is observed.
