Fate of a Reissner-Nordström black hole in the Einstein-Yang-Mills-Higgs system

We study an evaporating process of black holes in the SO(3) Einstein-Yang-Mills-Higgs system. We consider a massless scalar field which couples neither with the Yang-Mills field nor with the Higgs field surrounding the black hole. We discuss the differences in the evaporating rate between a monopole black hole and a Reissner-Nordström (RN) black hole. Since a RN black hole is unstable below the point at which a monopole black hole emerges, it will transit into a monopole black hole as suggested via catastrophe theory. We then conjecture the following: Starting from a Reissner-Nordström black hole, the mass decreases via the Hawking radiation and the black hole will reach a critical point. Then it transits to a monopole black hole. We find that the evaporation rate will increase continuously or discontinuously according to the type of phase transition that is either second order or first order, respectively. After its transition, the evaporation will never stop because the Hawking temperature of a monopole black hole diverges at the zero horizon limit and overcomes the decrease of the transmission amplitude Γ.