Thermodynamics at the BPS bound for black holes in AdS

In this work we define a new limiting procedure that extends the usualthermodynamics treatment of Black Hole physics, to the supersymmetric regime.This procedure is inspired on equivalent statistical mechanics derivations inthe dual CFT theory, where the BPS partition function at zero temperature isobtained by a double scaling limit of temperature and the relevant chemicalpotentials. In supergravity, the resulting partition function depends onemergent generalized chemical potentials conjugated to the different conservedcharges of the BPS solitons. With this new approach, studies on stability andphase transitions of supersymmetric solutions are presented. We find stable andunstable regimes with first order phase transitions, as suggested by previousstudies on free supersymmetric Yang Mills theory.Comment: 22 pages, 6 figures, latex, one reference added, typos corrected, final version for JHE