Depilating Global Charge From Thermal Black Holes
  At a formal level, there appears to be no difficulty involved in introducing a chemical potential for a globally conserved quantum number into the partition function for space-time including a black hole. Were this possible, however, it would provide a form of black hole hair, and contradict the idea that global quantum numbers are violated in black hole evaporation. We demonstrate dynamical mechanisms that negate the formal procedure, both for topological charge (Skyrmions) and complex scalar-field charge. Skyrmions collapse to the horizon; scalar-field charge fluctuates uncontrollably. 
John March-Russell, Frank Wilczek