  The possibility of a gravitational phase transition, especially with respect
to neutron stars is investigated. First, a semiclassical treatment is given,
predicting a gravitational London penetration depth of 12km for neutron stars.
Second, the problem is considered from a Ginzburg-Landau point of view. A
gravitational Meissner effect, a gravitational Aharanov-Bohm type effect and a
gravitational ferromagnetic type phase are predicted. Finally, a field
theoretic consideration predicts a mass term for the graviton below a certain
critical temperature.
