Some thermodynamic aspects of black holes and singularities

We review and correct the classical critical exponents characterizing the transition from negative to positive black hole's heat capacity at high charge-angular momentum. We discuss the stability properties of black holes as a thermodynamic system in equilibrium with a radiation bath (canonical ensemble) by using the Helmholtz free energy potential. Finally we analytically extend the analysis to any value of the variables in the Helmholtz potential and show that this leads to the consideration of negative mass holes. We then study their curious thermodynamical stability behavior.