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 .

PACS number ( s ) : 04.60 , 04.70 , 11.15.E , 97.60.J