Quantum Hair, Instantons, and Black Hole Thermodynamics: Some New   Results
  We present results obtained by a consideration of the non-classical energy momentum tensor associated with Euclidean Instantons outside the event horizon of black holes. We demonstrate here how this allows an analytic estimate to be made of the effect of discrete quantum hair on the temperature of the black hole, in which the role of violations of the weak energy condition associated with instantons is made explicit, and in which the previous results of Coleman, Preskill, and Wilczek are extended. Last, we demonstrate how the existence of a non-classical electric field outside the event horizon of black holes, uncovered by these authors, can be identified with a well-known effect in the Abelian-Higgs model in two dimensions. In this case, there is a one-to-one connection between the discrete charge of a black hole and a topological phase in two dimensions. 
Lawrence M. Krauss and Hong Liu (Case Western Reserve University)