Gravothermal instability with a cosmological constant in the canonical
  ensemble
  We present here how the gravothermal or Antonov's instability, which was
originally formulated in the microcanonical ensemble, is modified in the
presence of a cosmological constant and in the canonical ensemble. In contrast
to the microcanonical ensemble, there is a minimum, and not maximum, radius for
which metastable states exist. In addition this critical radius is decreasing,
and not increasing, with increasing cosmological constant. The minimum
temperature for which metastable states exist is decreasing with increasing
cosmological constant, while above some positive value of the cosmological
constant, there appears a second critical temperature. For lower temperatures
than the second critical temperature value, metastable states reappear,
indicating a typical reentrant phase transition. The two critical temperatures
merge when the cosmological density equals one half the mean density of the
system.
