Abstract
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.
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Cassani, D., Papini, L. The BPS limit of rotating AdS black hole thermodynamics. J. High Energ. Phys. 2019, 79 (2019). https://doi.org/10.1007/JHEP09(2019)079
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DOI: https://doi.org/10.1007/JHEP09(2019)079