For toric AdS4 black holes, the geometric entropy extremization of Gauntlett, Martelli and Sparks is shown to be equivalent to I-extremization with a generalized free energy built from the master volume, including baryonic charges.
Uplifting dyonic AdS$_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
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abstract
We revisit non-rotating, dyonically charged, and supersymmetric AdS$_4$ black holes, which are solutions of $\mathcal{N}=2$ gauged supergravity with vector- and hyper-multplets. Uplifting the near horizon solutions to $D=11$ supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS$_4$ black holes correspond to AdS$_2$ solutions with electric and magnetic baryonic fluxes in $D=11$ supergravity. We identify the off-shell AdS$_4$ black hole solutions with parameters of $D=11$ AdS$_2$ solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.
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$\mathcal{I}$-Extremization for AdS$_4$ Black Holes: Master Volume, Free Energy, and Baryonic Charges
For toric AdS4 black holes, the geometric entropy extremization of Gauntlett, Martelli and Sparks is shown to be equivalent to I-extremization with a generalized free energy built from the master volume, including baryonic charges.