Black holes with non-Abelian hair and their thermodynamical properties

We present some black-hole solutions of the Einstein-Yang-Mills-dilaton system and calculate their Hawking temperatures. We find that if the coupling constant of the dilation is smaller than some critical value, the thermodynamical behavior of these black holes includes two phase transitions at points determined by the value of the mass parameter. The black holes with masses between those two critical values have a positive specific heat. This is also true for the known colored black-hole solutions. We also reanalyze Skyrme black holes and find that there exist two types of solutions (a stable type and an unstable excited type) and these two types converge to a bifurcation point at some critical horizon radius, beyond which there is no Skyrme black hole. The stable black holes have two possible fates: they can evaporate via the Hawking process, and so evolve into a particlelike (Skyrmion) solution, or they can accrete matter and evolve into the Schwarzschild solution. When a Skyrme black hole evolves into a Schwarzschild black hole, its area changes discontinuously, so that we may regard this evolution as a kind of first-order phase transition. The specific heat of stable Skyrme black holes is always negative, while there are either one or three transition points for unstable Skyrme black holes.