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Gravitational Blocks: Symplectic Covariance Unveiled
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abstract
By working in a symplectically covariant real formulation of special K\"ahler geometry, we propose and give strong evidence for a canonical BPS partition function for AdS$_2 \times_w M_2$ near-horizon geometries with arbitrary rotation and generic magnetic and electric charges. Here, $M_2$ is either a two-sphere or a spindle. We also show that how the attractor equations and the Bekenstein-Hawking entropy can be obtained from an extremization principle.
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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 bar...
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