Phase transition in the Reissner-Nordstrom black hole

The thermodynamics of the Reissner-Nordstrom black hole at the charge-to-mass ratio of root 3/2 is studied. We show that there exists infinite discontinuity not only in the heat capacity but also in the electromagnetic potential and hence in the Gibbs free energy. Despite the existence of an infinite discontinuity in the heat capacity, it is shown that there exists no phase transition in the Reissner-Nordstrom black hole. The discontinuity may be merely an artefact of the change in the slope of the vertical bar Q vertical bar vs. M curve when the charge-to-mass ratio crosses root 3/2. This may signify that the horizon temperature is not a well-behaved thermodynamic parameter in the black hole thermodynamics.