where M is ADM mass of the black hole and N are the conserved charges and a runs from 1 to n. The signature of the metric reflects the sign of the hole's specific heat. For a Reissner–Nordström black hole, the Ruppeiner metric has a Lorentzian signature which corresponds to the negative heat capacity it possess, while for the BTZ black hole, we have a Euclidean signature. This calculation cannot be done for the Schwarzschild black hole, because its entropy is