The BPS limit of rotating AdS black hole thermodynamics

Understand

We consider rotating, electrically charged, supersymmetric AdS black holes in four, five, six and seven dimensions, and provide a derivation of the respective extremization principles stating that the Bekenstein-Hawking entropy is the Legendre transform of a homogeneous function of chemical potentials, subject to a complex constraint.

• Extending a recently proposed BPS limit, we start from finite temperature and reach extremality following a supersymmetric trajectory in the space of complexified solutions.
• We show that the entropy function is the supergravity on-shell action in this limit.
• Chemical potentials satisfying the extremization equations also emerge from the complexified solution.